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June, 1974 Uniform Inequalities for Conditional Expectations
L. Rogge
Ann. Probab. 2(3): 486-489 (June, 1974). DOI: 10.1214/aop/1176996664

Abstract

The purpose of this note is to show that Neveu's uniform inequality for conditional expectations can be sharpened and extended to arbitrary conditioning sub-$\sigma$-fields. An application of this inequality yields that a sequence of conditional expectations given a $\sigma$-field $\mathscr{F}_n$ converges uniformly for all test functions to a conditional expectation given a $\sigma$-field $\mathscr{F}_\infty$ if and only if the $\sigma$-fields $\mathscr{F}_n$ converge to $\mathscr{F}_\infty$ in the usual metric.

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L. Rogge. "Uniform Inequalities for Conditional Expectations." Ann. Probab. 2 (3) 486 - 489, June, 1974. https://doi.org/10.1214/aop/1176996664

Information

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

zbMATH: 0285.28010
MathSciNet: MR362417
Digital Object Identifier: 10.1214/aop/1176996664

Subjects:
Primary: 28A20
Secondary: 60645

Keywords: conditional expectation , inequality , metric for $\sigma$-fields

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 3 • June, 1974
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