Generalized conditional expectations

Author:
William E. Hornor

Journal:
Proc. Amer. Math. Soc. **123** (1995), 3681-3685

MSC:
Primary 28A99; Secondary 60A10

MathSciNet review:
1277115

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Abstract: In this paper, we state conditions sufficient for the existence of conditional expectations. Given a measure space and a -subalgebra , we give conditions on which insure that for every real-valued -measurable function *f* there exists a -measurable function such that for every -measurable function *g* for which the left integral exists. These conditions entail a notion of "fineness" of the subalgebra and a "completeness" property of . We then introduce a notion of generalized conditional expectation which requires only the former condition.

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1995-1277115-X

Article copyright:
© Copyright 1995
American Mathematical Society