Hostname: page-component-77c89778f8-gq7q9 Total loading time: 0 Render date: 2024-07-22T01:46:02.633Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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