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On the Equivalence of Modes of Convergence(1)

Published online by Cambridge University Press:  20 November 2018

R. J. Tomkins
R. J. Tomkins*
Affiliation:
University of Saskatchewan Regina Campus, Regina, Saskatchewan
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Let (Ω,ℱ, P) be a probability space. Let R denote the set of real numbers and the set of all random variables defined on Ω. Throughout this work, random variables which differ only on a set of probability zero will be considered identical. EX represents, as usual, the expectation of .

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 4 , December 1973 , pp. 571 - 575
Copyright
Copyright © Canadian Mathematical Society 1973

Footnotes

(1)

The author is grateful to the National Research Council for financial support during the preparation of this work.

References

1. Hsu, P. L. and Robbins, Herbert, Complete convergence and the law of large numbers, Proc. Acad. Sci. U.S.A. 33 (1947), 25–31.Google Scholar
2. Loève, M., Probability theory, 3rd edition, Van Nostrand, Princeton, N.J., 1963.Google Scholar
3. Thomasian, A. J., Metrics and norms on spaces of random variables, Ann. Math. Statist. 28 (1957), 512–514.Google Scholar