Uniform convergence of distribution functions

Eisenberg, Bennett; Gan, Shi Xin

doi:10.1090/S0002-9939-1983-0691296-X

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Uniform convergence of distribution functions
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by Bennett Eisenberg and Shi Xin Gan

Proc. Amer. Math. Soc. 88 (1983), 145-146

DOI: https://doi.org/10.1090/S0002-9939-1983-0691296-X

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Abstract:

Necessary and sufficient conditions are given for uniform convergence of probability distribution functions.

References

Yuan Shih Chow and Henry Teicher, Probability theory, Springer-Verlag, New York-Heidelberg, 1978. Independence, interchangeability, martingales. MR 513230
F. J. Dyson, Fourier transforms of distribution functions, Canad. J. Math. 5 (1953), 554–558. MR 57362, DOI 10.4153/cjm-1953-062-x
Tatsuo Kawata, Fourier analysis in probability theory, Probability and Mathematical Statistics, No. 15, Academic Press, New York-London, 1972. MR 0464353