Short Proofs of Two Convergence Theorems for Conditional Expectations
Dieter Landers, Lothar Rogge · The Annals of Mathematical Statistics · 1972
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 $P_n$.