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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 22, Fasc. 1,
pages 115 - 126
 

ON THE SEQUENCES WHOSE CONDITIONAL EXPECTATIONS CAN APPROXIMATE ANY RANDOM VARIABLE

Krzysztof Kaniowski

Abstract: Let (_O_,F,P) be a non-atomic probability space. For a given sequence (X ) n of random variables we indicate a number of conditions which imply that for any random variable Y there exists a sequence (U ) n of s -fields satisfying E(X | U )-- > Y n n a.s. In particular, we formulate a sufficient condition using the distributions of X n ’s only.

2000 AMS Mathematics Subject Classification: 60A10.

Key words and phrases: Conditional expectation, almost sure convergence.

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