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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Admissible and singular translates of measures on vector spaces
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by Alan Gleit and Joel Zinn
Trans. Amer. Math. Soc. 221 (1976), 199-211
DOI: https://doi.org/10.1090/S0002-9947-1976-0436244-3
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Abstract:

We provide a general setting for studying admissible and singular translates of measures on linear spaces. We apply our results to measures on $D[0,1]$. Further, we show that in many cases convex, balanced, bounded, and complete subsets of the admissible translates are compact. In addition, we generalize Sudakov’s theorem on the characterization of certain quasi-invariant sets to separable reflexive spaces which have the Central Limit Property.
References
  • R. M. Dudley, Singular translates of measures on linear spaces, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 3 (1964), 128–137 (1964). MR 169277, DOI 10.1007/BF00535972
  • R. Fortet and E. Mourier, Les fonctions alĂ©atoires comme Ă©lĂ©ments alĂ©atoires dans les espaces de Banach, Studia Math. 15 (1955), 62–79 (French). MR 93052, DOI 10.4064/sm-15-1-62-79
    • J. Hoffmann-JĂžrgensen and G. Pisier, The law of large numbers and the central limit theorem in Banach spaces (preprint).
  • J. L. Kelley and Isaac Namioka, Linear topological spaces, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J., 1963. With the collaboration of W. F. Donoghue, Jr., Kenneth R. Lucas, B. J. Pettis, Ebbe Thue Poulsen, G. Baley Price, Wendy Robertson, W. R. Scott, Kennan T. Smith. MR 0166578
  • J. Kuelbs, Gaussian measures on a Banach space, J. Functional Analysis 5 (1970), 354–367. MR 0260010, DOI 10.1016/0022-1236(70)90014-5
  • Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces, Lecture Notes in Mathematics, Vol. 338, Springer-Verlag, Berlin-New York, 1973. MR 0415253
  • A. Pietsch, Absolut $p$-summierende Abbildungen in normierten RĂ€umen, Studia Math. 28 (1966/67), 333–353 (German). MR 216328, DOI 10.4064/sm-28-3-333-353
  • A. P. Robertson and Wendy Robertson, Topological vector spaces, 2nd ed., Cambridge Tracts in Mathematics and Mathematical Physics, No. 53, Cambridge University Press, London-New York, 1973. MR 0350361
  • V. N. Sudakov, On the characterization of the quasi-invariance of measures in Hilbert space, Uspehi Mat. Nauk 18 (1963), no. 1, 188–190 (Russian). MR 0149250
  • Dao Xing Xia, Measure and integration theory on infinite-dimensional spaces. Abstract harmonic analysis, Pure and Applied Mathematics, Vol. 48, Academic Press, New York-London, 1972. Translated by Elmer J. Brody. MR 0310179
  • Joel Zinn, Admissible translates of stable measures, Studia Math. 54 (1975/76), no. 3, 245–257. MR 400376, DOI 10.4064/sm-54-3-245-257
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Bibliographic Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 221 (1976), 199-211
  • MSC: Primary 60B05; Secondary 28A40, 60G30
  • DOI: https://doi.org/10.1090/S0002-9947-1976-0436244-3
  • MathSciNet review: 0436244