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A Stone-Weierstrass theorem for random functions

Published online by Cambridge University Press:  17 April 2009

A. Mukherjea
A. Mukherjea
Affiliation:
University of South Florida, Tampa, Florida, USA.
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Abstract

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It is shown in this note that if Q is an algebra of uniformly bounded mean-square continuous real-valued random functions indexed in a compact set T, containing all bounded random variables and separating points of T (i.e., given t1 and t2 in T, there is a random function Xt in Q such that , then given any mean square continuous random function, there is a sequence in Q converging in mean square to the given random function uniformly on T.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 2 , Issue 2 , April 1970 , pp. 233 - 236
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Dieudonné, J., Foundations of modern analysis (Academic Press, New York, London, 1960).Google Scholar
[2]Tzannes, Nicolaos S., “Polynomial expansions of random functions”, IEEE Trans. Information Theory 11–13 (1967), 314.CrossRefGoogle Scholar