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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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Differentiation theorem for Gaussian measures on Hilbert space
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by Jaroslav Tišer PDF
Trans. Amer. Math. Soc. 308 (1988), 655-666 Request permission

Abstract:

It is shown that the differentiation theorem is valid in infinitely dimensional Hilbert space with certain Gaussian measures. The proof uses result from harmonic analysis concerning the behavior of Hardy-Littlewood maximal operator in highly dimensional space.
References
  • D. Preiss, Gaussian measures and covering theorems, Comment. Math. Univ. Carolin. 20 (1979), no. 1, 95–99. MR 526149
  • D. Preiss, Gaussian measures and the density theorem, Comment. Math. Univ. Carolin. 22 (1981), no. 1, 181–193. MR 609946
  • David Preiss, Differentiation of measures in infinitely-dimensional spaces, Proceedings of the Conference Topology and Measure III, Part 1, 2 (Vitte/Hiddensee, 1980) Wissensch. Beitr., Ernst-Moritz-Arndt Univ., Greifswald, 1982, pp. 201–207. MR 677136
  • D. Preiss and J. Tišer, Differentiation of Gaussian measures on Hilbert space, Lecture Notes Math., vol. 945, Springer-Verlag, Berlin and New York, 1981, pp. 194-207.
  • E. M. Stein and J.-O. Strömberg, Behavior of maximal functions in $\textbf {R}^{n}$ for large $n$, Ark. Mat. 21 (1983), no. 2, 259–269. MR 727348, DOI 10.1007/BF02384314
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 308 (1988), 655-666
  • MSC: Primary 28C20; Secondary 28A15, 46G12
  • DOI: https://doi.org/10.1090/S0002-9947-1988-0951621-8
  • MathSciNet review: 951621