Open Access
Translator Disclaimer
June, 1974 Convexity and Conditional Expectations
J. Pfanzagl
Ann. Probab. 2(3): 490-494 (June, 1974). DOI: 10.1214/aop/1176996665

Abstract

If a $n$-dimensional function is with probability one in a convex set, the same holds true for the conditional expectation (with respect to any sub-$\sigma$-field). An extreme point of this convex set can be assumed by the conditional expectation only if it is assumed by the original function and if this function is partially measurable with respect to the conditioning sub-$\sigma$-field. These results are used to prove Jensen's inequality for conditional expectations of $n$-dimensional functions, and to give a condition for strict inequality.

Citation

Download Citation

J. Pfanzagl. "Convexity and Conditional Expectations." Ann. Probab. 2 (3) 490 - 494, June, 1974. https://doi.org/10.1214/aop/1176996665

Information

Published: June, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0285.60002
MathSciNet: MR358893
Digital Object Identifier: 10.1214/aop/1176996665

Subjects:
Primary: 62B99
Secondary: 52A40

Keywords: Conditional expectations , convex sets

Rights: Copyright © 1974 Institute of Mathematical Statistics

JOURNAL ARTICLE
5 PAGES


SHARE
Vol.2 • No. 3 • June, 1974
Back to Top