The Annals of Mathematical Statistics

Short Proofs of Two Convergence Theorems for Conditional Expectations

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

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