A note on the weak convergence of continuously integrable sequences
Functional Analysis
2021-08-10 v1
Abstract
A uniformly continuously integrable sequence of real-valued measurable functions, defined on some probability space, is relatively compact in the topology. In this paper, we link such a result to weak convergence theory of bounded measures as exposed in Billingsley (1968) and in Lo(2021) to offer a detailed and new proof using the ideas beneath the proof of prohorov's theorem where the continuous integrability replaces the uniform or asymptotic tightness.
Cite
@article{arxiv.2108.03484,
title = {A note on the weak convergence of continuously integrable sequences},
author = {Gane Samb Lo and Aladji Babacar Niang},
journal= {arXiv preprint arXiv:2108.03484},
year = {2021}
}