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A Stone-Weierstrass theorem for random functions
Published online by Cambridge University Press: 17 April 2009
Abstract
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.
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- Copyright © Australian Mathematical Society 1970
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