motapa - William Feller's Bibliography


Scientific Publications of William Feller

The following list is based on the bibliography compiled in the Selecta of William Feller  Selected Papers (2 vol) edited by R. Schilling, Z. Vondraček and W. Woyczyński (Springer, Cham 2015) . The DOIs and Links provided give access to the relevant publication as long as your IP-Number has access rights (e.g. by subscription to the relevant journal or archive).
  1. Über algebraisch rektifizierbare transzendente Kurven [On algebraically rectifiable transcendental curves].
    PhD-Thesis Universität Göttingen, June 1926. Advisor: Richard Courant. Also published as [2]
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  2. Über algebraisch rektifizierbare transzendente Kurven [On algebraically rectifiable transcendental curves].
    Mathematische Zeitschrift
    27 (1928) 481-495.
    DOI: 10.1007/BF01171108
  3. Über die Lösungen der linearen partiellen Differentialgleichungen zweiter Ordnung vom elliptischen Typus [On the solutions of second-order
    linear partial differential equations of elliptic type].
    Habilitationsschrift Universität Kiel, February 1929. Also published as [4]
  4. Über die Lösungen der linearen partiellen Differentialgleichungen zweiter Ordnung vom elliptischen Typus [On the solutions of second-order
    linear partial differential equations of elliptic type].
    Mathematische Annalen 102 (1930) 633-649.
    DOI: 10.1007/BF01782367
  5. (with Erhard Tornier) Mengentheoretische Untersuchung von Eigenschaften der Zahlenreihe [Set-theoretic investigation of some properties of the natural numbers].
    Zentralblatt 1 (1931) 257–259.
  6. (with Erhard Tornier) Maß- und Inhaltstheorie des Baireschen Nullraumes [Measure and integration theory of Baire’s null space].
    Mathematische Annalen 107 (1932) 165–187.
    DOI: http://dx.doi.org/10.1007/BF01448889
  7. (with Erhard Tornier) Mengentheoretische Untersuchung von Eigenschaften der Zahlenreihe [Set-theoretic investigation of some properties of
    the natural numbers].
    Mathematische Annalen 107 (1932) 188–232.
    DOI: http://dx.doi.org/10.1007/BF01448890
  8. Allgemeine Maßtheorie und Lebesguesche Integration [General measure theory and Lebesgue integration].
    Sitzungsberichte der Preußischen Akademie derWissenschaften, Physikalisch–Mathematische Klasse 27 (1932) 459–472.
  9. (with Herbert Busemann) Zur Differentiation der Lebesgueschen Integrale [On the differentiation of Lebesgue’s integrals].
    Fundamenta Mathematicae 22 (1934) 226-256.
    Link to the journal
  10. Bemerkungen zur Maßtheorie in abstrakten Räumen [Remarks on measure theory in abstract spaces].
    Bulletin international de l’académie Yougoslave des sciences et des beaux-arts, Zagreb. Classe des sciences mathématiques et naturelles 28 (1934) 30–45.
    Croatian original publication: Dr. Vilim (W.) Feller: Prilog teoriji mjera u apstraktnim prostorima. RAD 249 (1934) 204–224.
  11. (with Herbert Busemann) Bemerkungen zur Differentialgeometrie der konvexen Flächen. I. Kürzeste Linien auf differenzierbaren Flächen [Remarks
    on the differential geometry of convex surfaces. I. Shortest lines on differentiable surfaces].
    Matematisk Tidsskrift B (1935) 25–36.
  12. (with Herbert Busemann) Bemerkungen zur Differentialgeometrie der konvexen Flächen. II. Über die Krümmungsindikatrizen [Remarks on
    the differential geometry of convex surfaces. II. On curvature indicatrices].
    Matematisk Tidsskrift B (1935) 87–115.
  13. Über den zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung [On the central limit theorem of probability theory].
    Mathematische Zeitschrift 40 (1936) 521-559.
    DOI: 10.1007/BF01218878
  14. (with Herbert Busemann) Bemerkungen zur Differentialgeometrie der konvexen Flächen. III. Über die Gauss’sche Krümmung [Remarks on the
    differential geometry of convex surfaces. III. On Gauss’ curvature].
    Matematisk Tidsskrift B (1936) 41–70.
  15. (with Herbert Busemann) Krümmungseigenschaften konvexer Flächen.[Curvature properties of convex surfaces]
    Acta Mathematica 66 (1936) 1-47.
    DOI: 10.1007/BF02546515
  16. Zur Theorie der stochastischen Prozesse. (Existenz- und Eindeutigkeitssätze). [On the theory of stochastic processes. (Existence and Uniqueness theorems)].
    Mathematische Annalen 113 (1936) 113-160.
    DOI: 10.1007/BF01571626
  17. Über den zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung. II [On the central limit theorem of probability theory. II].
    Mathematische Zeitschrift 42 (1937) 301-312.
    DOI: 10.1007/BF01160080
    Erratum. Mathematische Zeitschrift 44 (1939) 794.
    DOI: 10.1007/BF01210684
  18. Über das Gesetz der großen Zahlen [On the law of large numbers].
    Acta Litterarum ac Scientiarum. Regiae Universitatis Hungaricae Francisco-Josephinae. Sectio Scientiarum Mathematicarum. (Acta. Sci. Litt. Szeged) 8 (1937) 191-201.
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  19. Über die Theorie der stochastischen Prozesse [On the theory of stochastic processes].
    In: Comptes Rendus du Congrès International des Mathématiciens. Oslo 1936. Vol. 2. A. W. Brøggers Boktrykkeri A/S, Oslo 1937, pp. 194–196.
  20. Sur les axiomatiques du calcul des probabilités et leurs relations avec les expériences [On the axioms of probability theory and their relations with
    the experience].
    In: P. Cantelli, M. Fréchet, R. von Mises, I. F. Steffensen and A.Wald (eds.): Conférences internationales de sciences mathématiques.
    Colloque consacré à la théorie des probabilités. II: Les fondements du calcul des probabilités.
    Actualités scientifiques et industrielles 735. Hermann & Cie., Paris 1938, pp. 7–21.
  21. Note on regions similar to the sample space.
    Statistical Research Memoirs, University College London 2 (1938), 117–125.
  22. (with J. Runnström and E. Sperber) Die Aufnahme von Glucose durch Bäckerhefe unter aeroben und anaeroben Bedingungen [On the absorption
    of glucose by baker’s yeast under aerobic and anaerobic conditions].
    Naturwissenschaften 26 (1938) 547–548.
  23. Die Grundlagen der Volterraschen Theorie des Kampfes ums Dasein in wahrscheinlichkeitstheoretischer Behandlung [The foundations of
    Volterra’s theory on the struggle for life in a probabilistic treatment].
    Acta Biotheoretica, Leiden 5 (1939) 11-39.
    DOI: 10.1007/BF01602932
  24. Completely monotone functions and sequences.
    Duke Mathematical Journal 5 (1939) 661-674.
    DOI: 10.1215/S0012-7094-39-00555-7
  25. Über die Existenz von sogenannten Kollektiven [On the existence of so-called Kollektivs].
    Fundamenta Mathematicae 32 (1939) 87-96.
    Link to the journal
  26. Neuer Beweis für die Kolmogoroff-P. Lévysche Charakterisierung der unbeschränkt teilbaren Verteilungsfunktionen [A new proof of Kolmogoroff’s and P. Levy’s characterization of infinitely divisible distribution functions].
    Bulletin international de l'académie Yougoslave des sciences et des beaux-arts, Zagreb. Classe des sciences mathématiques et naturelles 32 (1939) 106-113. 
  27. On the logistic law of growth and its empirical verifications in biology.
    Acta Biotheoretica, Leiden 5 (1940) 51–65.
    DOI: http://dx.doi.org/10.1007/BF01602862
  28. On the time distribution of so-called random events.
    Physical Reviews, II. Series 57 (1940) 906–908.
    DOI: http://dx.doi.org/10.1103/PhysRev.57.906
  29. On the integro-differential equations of purely discontinuous Markoff processes.
    Transactions of the American Mathematical Society 48 (1940) 488-515.
    DOI: 10.1090/S0002-9947-1940-0002697-3
  30. Statistical aspects of ESP.
    Journal of Parapsychology 4 (1940) 271–298.
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  31. On the integral equation of renewal theory.
    Annals of Mathematical Statistics 12 (1941) 243-267.
    DOI: 10.1214/aoms/1177731708
  32. (with Jacob David Tamarkin) Partial Differential Equations. Brown University Summer Session for Advanced Instructions & Research in Mechanics. 6/23- 9/13 1941, Providence (RI) 1941. Chapters 1–3 by J. D. Tamarkin, Chapters 4–7 by William Feller.
    Reprinted by the Lewis Flight Propulsion Laboratory, National Committee for Aeronautics, Cleveland 1956.
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  33. Some geometric inequalities.
    Duke Mathematical Journal 9 (1942) 885-892.
    DOI: 10.1215/S0012-7094-42-00963-3
  34. On A. C. Aitken’s method of interpolation.
    Quarterly of Applied Mathematics 1 (1943) 86–87.
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  35. Generalization of a probability limit theorem of Cramér.
    Transactions of the American Mathematical Society 54 (1943) 361-372.
    DOI: 10.1090/S0002-9947-1943-0009262-5
  36. The general form of the so-called law of the iterated logarithm.
    Transactions of the American Mathematical Society 54 (1943) 373-402.
    DOI: 10.1090/S0002-9947-1943-0009263-7
  37. On a general class of "contagious" distributions.
    Annals of Mathematical Statistics 14 (1943) 389-400.
    DOI: 10.1214/aoms/1177731359
  38. On the normal approximation to the binomial distribution.
    Annals of Mathematical Statistics 16 (1945) 319-329.
    DOI: 10.1214/aoms/1177731058
  39. The fundamental limit theorems in probability.
    Bulletin of the American Mathematical Society 51 (1945) 800-832.
    DOI: 10.1090/S0002-9904-1945-08448-1
  40. (with Herbert Busemann) Regularity properties of a certain class of surfaces.
    Bulletin of the American Mathematical Society 51 (1945) 583-598.
    DOI: 10.1090/S0002-9904-1945-08403-1
  41. Note on the law of large numbers and "fair" games.
    Annals of Mathematical Statistics 16 (1945) 301-304.
    DOI: 10.1214/aoms/1177731094
  42. A limit theorem for random variables with infinite moments.
    American Journal of Mathematics 68 (1946) 257-262.
    DOI: 10.2307/2371837
  43. The law of the iterated logarithm for identically distributed random variables.
    Annals of Mathematics 47 (1946) 631-638.
    DOI: 10.2307/1969225
  44. On the Kolmogorov-Smirnov limit theorems for empirical distributions.
    Annals of Mathematical Statistics 19 (1948) 177-189.
    DOI: 10.1214/aoms/1177730243
    Erratum. Annals of Mathematical Statistics 21 (1950) 301-302.
    DOI: 10.1214/aoms/1177729850
  45. Spanish Translation of the paper [40]
    Revista Matemática Hispano-Americana, IV. Seria 8 (1948) 95–132.
  46. On probability problems in the theory of counters.
    In: Studies, Essays, presented to R. Courant (Courant anniversary volume) Interscience Publishers, New York 1948, pp. 105-115.
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  47. (with Paul Erdös and Harry Pollard) A property of power series with positive coefficients.
    Bulletin of the American Mathematical Society 55 (1949) 201-204.
    DOI: 10.1090/S0002-9904-1949-09203-0
  48. (with Kai Lai Chung) On fluctuations in coin-tossing.
    Proceedings of the National Academy of Sciences, USA 35 (1949) 605-608.
    DOI: 10.1073/pnas.35.10.605
  49. On the theory of stochastic processes, with particular reference to applications.
    In: J. Neyman (ed.): Proceedings of the (First) Berkeley Symposium on Mathematical Statistics and Probability 1945/46. University of California Press, Berkeley, Los Angeles 1949, pp. 403-432.
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  50. Fluctuation theory of recurrent events.
    Transactions of the American Mathematical Society 67 (1949) 98-119.
    DOI: 10.1090/S0002-9947-1949-0032114-7
  51. An Introduction to Probability Theory and Its Applications.
    John Wiley & Sons, New York 1950.
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  52. The asymptotic distribution of the range of sums of independent random variables.
    Annals of Mathematical Statistics 22 (1951) 427-432.
    DOI: 10.1214/aoms/1177729589
  53. (with George E. Forsythe) New matrix transformations for obtaining characteristic vectors.
    Quarterly of Applied Mathematics 8 (1951) 325–331.
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  54. The problem of n liars and Markov chains.
    American Mathematical Monthly 58 (1951) 606–608.
    DOI: http://dx.doi.org/10.2307/2306351
  55. Diffusion processes in genetics.
    In: J. Neyman (ed.): Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability 1950. University of California Press, Berkeley, Los Angeles (CA) 1951, pp. 227-246.
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  56. Two singular diffusion problems.
    Annals of Mathematics 54 (1951) 173-182.
    DOI: 10.2307/1969318
  57. The parabolic differential equations and the associated semigroups of transformation.
    Annals of Mathematics 55 (1952) 468-519.
    DOI: 10.2307/1969644
  58. On a generalization of Marcel Riesz' potentials and the semigroups generated by them.
    In: Meddelanden från Lunds Universitets Matematiska Seminarium. Supplement M. Riesz, Uppsala 1952, pp. 73-81.
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  59. Some recent trends in the mathematical theory of diffusion.
    In: Proceedings of the International Congress of Mathematicians, Cambridge (MA) 1950. Vol. 2. American Mathematical Society, Providence (RI) 1952, pp. 322-339.
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  60. (with George E. Forsythe) New matrix transformations for obtaining characteristic vectors.
    In: Proceedings of the International Congress of Mathematicians, Cambridge (MA) 1950. Vol. 1. American Mathematical Society, Providence (RI) 1952, p. 661.
  61. On positivity preserving semigroups of transformations on C[r1,r2].
    Annales de la Société Polonaise de Mathématique 25 (1952) 85-94.
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  62. Semigroups of transformations in general weak topologies.
    Annals of Mathematics 57 (1953) 287-308.
    DOI: 10.2307/1969859
  63. On the generation of unbounded semigroups of bounded linear operators.
    Annals of Mathematics 58 (1953) 166-174.
    DOI: 10.2307/1969826
  64. The general diffusion operator and positivity preserving semigroups in one dimension.
    Annals of Mathematics 60 (1954) 417-436.
    DOI: 10.2307/1969842
  65. Diffusion processes in one dimension.
    Transactions of the American Mathematical Society 77 (1954) 1-31.
    DOI: 10.1090/S0002-9947-1954-0063607-6
  66. On second order differential operators.
    Annals of Mathematics 61 (1955) 90-105.
    DOI: 10.2307/1969621
  67. On differential operators and boundary conditions.
    Communications on Pure and Applied Mathematics 8 (1955) 203-216.
    DOI: 10.1002/cpa.3160080112
  68. Boundaries induced by non-negative matrices.
    Transactions of the American Mathematical Society 83 (1956) 19-54.
    DOI: 10.1090/S0002-9947-1956-0090927-3
  69. (with Henry P. McKean Jr.) A diffusion equivalent to a countable Markov chain.
    Proceedings of the National Academy of Sciences, USA 42 (1956) 351-354.
    DOI: 10.1073/pnas.42.6.351
  70. (with Joanne Elliott) Stochastic processes connected with harmonic functions.
    Transactions of the American Mathematical Society 82 (1956) 392-420.
    DOI: 10.1090/S0002-9947-1956-0086440-X
  71. On generalized Sturm–Liouville operators.
    In: J. B. Diaz and L. E. Payne (eds.): Proceedings of the Conference on Differential Equations (Dedicated to A. Weinstein), University of Maryland Book Store, College Park (MD) 1956, pp. 251–270.
  72. Generalized second order differential operators and their lateral conditions.
    Illinois Journal of Mathematics 1 (1957) 459-504.
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  73. The numbers of zeros and of changes of sign in a symmetric random walk.
    L’Enseignement Mathématique, IIe. Série 3 (1957) 229–235.
  74. Sur une forme intrinsèque pour les opérateurs différentiels du second ordre [On an intrinsic form of second-order differential operators].
    Publications de l’Institut de Statistique de l’Université de Paris. Université de Paris VI, Institut de Statistique, Paris 6 (1957) 291–301.
  75. On boundaries and lateral conditions for the Kolmogorov differential equations.
    Annals of Mathematics 65 (1957) 527-570.
    DOI: 10.2307/1970064
    Additional notes. Annals of Mathematics 68 (1958) 735-736.
    DOI: 10.2307/1970166
  76. On boundaries defined by stochastic matrices.
    In: Proceedings of Symposia in Applied Mathematics. Vol. 7. McGraw-Hill Book Co., New York (for the American Mathematical Society, Providence (RI)) 1957, 35-40.
    DOI: 10.1090/psapm/007
  77. An Introduction to Probability Theory and Its Applications. Vol. 1.
    2nd edn. of [51]. John Wiley & Sons, New York 1957.
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  78. On the intrinsic form for second order differential operators.
    Illinois Journal of Mathematics 2 (1958) 1-18.
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  79. On combinatorial methods in fluctuation theory. 
    In: U. Grenander (ed.): The Harald Cramér Volume. Almqvist & Wiksell, Stockholm; John Wiley & Sons, New York 1959, pp. 75–91.
  80. The birth and death processes as diffusion processes.
    Journal de Mathématiques pures et appliquées, IX. série 38 (1959) 301-345.
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  81. Non-Markovian processes with the semigroup property.
    Annals of Mathematical Statistics 30 (1959) 1252-1253.
    DOI: 10.1214/aoms/1177706110
  82. Differential operators with the positive maximum property.
    Illinois Journal of Mathematics 3 (1959) 182-186.
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  83. On the equation of the vibrating string.
    Journal of Mathematics and Mechanics 8 (1959) 339–348.
    DOI: http://dx.doi.org/10.1512/iumj.1959.8.58023
  84. Some new connections between probability and classical analysis.
    Proceedings of the International Congress of Mathematicians, Edinburgh 1958. Cambridge University Press, Cambridge 1960, pp. 69-86.
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  85. (with Steven Orey) A renewal theorem.
    Journal of Mathematics and Mechanics 10 (1961) 619-624.
    DOI: 10.1512/iumj.1961.10.10041
  86. A simple proof for renewal theorems.
    Communications on Pure and Applied Mathematics 14 (1961) 285-293.
    DOI: 10.1002/cpa.3160140308
  87. Chance processes and fluctuations.
    In: E. F. Beckenbach and M. R. Hestenes (eds.): Modern Mathematics for the Engineer: Second Series. University of California Engineering Extension Series. Mc Graw-Hill, New York 1961, pp. 167–181.
  88. On the classical Tauberian theorems.
    Archiv der Mathematik 14 (1963) 317-322.
    DOI: 10.1007/BF01234960
  89. On semi-Markov processes.
    Proceedings of the National Academy of Sciences, USA 51 (1964) 653-659.
    DOI: 10.1073/pnas.51.4.653
  90. On the Fourier representation for Markov chains and the strong ratio theorem.
    Journal of Mathematics and Mechanics 15 (1966) 273-283.
    DOI: 10.1512/iumj.1966.15.15019
  91. On the influence of natural selection on population size.
    Proceedings of the National Academy of Sciences, USA 55 (1966) 733-738.
    DOI: 10.1073/pnas.55.4.733
  92. Infinitely divisible distributions and Bessel functions associated with random walks.
    SIAM Journal of Applied Mathematics 14 (1966) 864-875.
    DOI: 10.1137/0114071
  93. An Introduction to Probability Theory and Its Applications. Vol. 2.
    John Wiley & Sons, New York 1966.
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  94. On regular variation and local limit theorems.
    In: J. Neyman and L. LeCam (eds.): Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability 1965/66, Vol. 2, Pt. 1, University of California Press, Berkeley, Los Angeles (Ca) 1967, pp. 373-388.
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  95. A direct proof of Stirling’s formula.
    American Mathematical Monthly 74 (1967) 1223–1225.
    DOI: http://dx.doi.org/10.2307/2315671
    Erratum: American Mathematical Monthly 75 (1968) 518.
    DOI: http://dx.doi.org/10.2307/2314719
  96. On fitness and the cost of natural selection.
    Genetics Research 9 (1967) 1-15.
    DOI: 10.1017/S0016672300010260
  97. On Müntz’ theorem and completely monotone functions.
    American Mathematical Monthly 75 (1968) 342–350.
    DOI: http://dx.doi.org/10.2307/2313410
  98. On the Berry-Esseen theorem.
    Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 10 (1968) 261-268.
    DOI: 10.1007/BF00536279
  99. On probabilities of large deviations.
    Proceedings of the National Academy of Sciences, USA 61 (1968) 1224–1227.
    DOI: http://dx.doi.org/10.1073/pnas.61.4.1224
  100. An extension of the law of the iterated logarithm to variables without variance.
    Journal of Mathematics and Mechanics 18 (1968) 343-355.
    DOI: 10.1512/iumj.1969.18.18027
  101. An Introduction to Probability Theory and Its Applications. Vol. 1.
    3rd edn. of [51], [77]. John Wiley & Sons, New York 1968.
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  102. A geometrical analysis of fitness in triply allelic systems.
    Mathematical Biosciences 5 (1969) 19–38.
    DOI: http://dx.doi.org/10.1016/0025-5564(69)90033-9
  103. One-sided analogues of Karamata's regular variation.
    L'Enseignement Mathématique, IIe. Serie 15 (1969) 107-121.
    DOI: 10.5169/seals-43209
  104. Limit theorems for probabilities of large deviations.
    Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 14 (1969) 1-20.
    DOI: 10.1007/BF00534113
  105. General analogues to the law of the iterated logarithm.
    Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 14 (1969) 21-26.
    DOI: 10.1007/BF00534114
  106. On the fluctuations of sums of independent random variables.
    Proceedings of the National Academy of Sciences, USA 63 (1969) 637–639.
    DOI: http://dx.doi.org/10.1073/pnas.63.3.637
  107. Are life scientists overawed by Statistics? (Too much faith in statistics).
    Scientific Research 4.3 (1969) 24–29.
  108. On the oscillations of sums of independent random variables.
    Annals of Mathematics 91 (1970) 402-418.
    DOI: 10.2307/1970583
  109. An Introduction to Probability Theory and Its Applications. Vol. 2.
    2nd edn. of [93]. John Wiley & Sons, New York 1971. Posthumously published. The final version was published with the help of J. Goldman, A. Grunbaum, H. P. McKean, L. Pitt and A. Pittenger.
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