The Annals of Mathematical Statistics

Short Proofs of Two Convergence Theorems for Conditional Expectations

D. Landers and L. Rogge

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Abstract

In this paper there are given new proofs of two convergence theorems for conditional expectations, concerning convergence in measure and convergence almost everywhere of a sequence of conditional expectations $P_n^\mathscr{F}0f$ of a bounded function $f$, given a $\sigma$-field $\mathscr{F}_0$, with respect to varying probability measures $P_n$.

Article information

Source
Ann. Math. Statist., Volume 43, Number 4 (1972), 1372-1373.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177692493

Digital Object Identifier
doi:10.1214/aoms/1177692493

Mathematical Reviews number (MathSciNet)
MR315748

Zentralblatt MATH identifier
0241.60022

JSTOR
links.jstor.org

Citation

Landers, D.; Rogge, L. Short Proofs of Two Convergence Theorems for Conditional Expectations. Ann. Math. Statist. 43 (1972), no. 4, 1372--1373. doi:10.1214/aoms/1177692493. https://projecteuclid.org/euclid.aoms/1177692493


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