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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On a necessary and sufficient condition that an infinitely divisible distribution be absolutely continuous
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by Howard G. Tucker PDF
Trans. Amer. Math. Soc. 118 (1965), 316-330 Request permission
  • J. R. Blum and Murray Rosenblatt, On the structure of infinitely divisible distributions, Pacific J. Math. 9 (1959), 1–7. MR 105729
  • Marek Fisz, Infinitely divisible distributions: recent results and applications, Ann. Math. Statist. 33 (1962), 68–84. MR 139188, DOI 10.1214/aoms/1177704712
  • M. Fisz and V. S. Varadarajan, A condition for absolute continuity of infinitely divisible distribution functions, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 1 (1962/63), 335–339. MR 149521, DOI 10.1007/BF00533408
  • B. V. Gnedenko and A. N. Kolmogorov, Limit distributions for sums of independent random variables, Addison-Wesley Publishing Co., Inc., Cambridge, Mass., 1954. Translated and annotated by K. L. Chung. With an Appendix by J. L. Doob. MR 0062975
  • Philip Hartman and Aurel Wintner, On the infinitesimal generators of integral convolutions, Amer. J. Math. 64 (1942), 273–298. MR 6635, DOI 10.2307/2371683
  • Jean-Pierre Kahane and Raphaël Salem, Ensembles parfaits et séries trigonométriques, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1301, Hermann, Paris, 1963 (French). MR 0160065
  • Michel Loève, Probability theory, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-New York-London, 1960. 2nd ed. MR 0123342
  • Eugene Lukacs, Characteristic functions, Griffin’s Statistical Monographs & Courses, No. 5, Hafner Publishing Co., New York, 1960. MR 0124075
  • H. Rubin, Supports of infinitely divisible distributions, Tech. Rep. No. RM-108 HR-10, Michigan State Univ., Department of Statistics, East Lansing, Mich., 1963.
  • Howard G. Tucker, Absolute continuity of infinitely divisible distributions, Pacific J. Math. 12 (1962), 1125–1129. MR 146868
  • Howard G. Tucker, On continuous singular infinitely divisible distribution functions, Ann. Math. Statist. 35 (1964), 330–335. MR 161362, DOI 10.1214/aoms/1177703755
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Additional Information
  • © Copyright 1965 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 118 (1965), 316-330
  • MSC: Primary 60.20
  • DOI:
  • MathSciNet review: 0182061