Uniform Integrability in vector lattices and applications
Functional Analysis
2023-04-17 v1
Abstract
In this paper, we explore an abstraction of uniform integrability in vector lattices and demonstrate its application by providing a positive solution to an open question posed by Kuo, Rodda, and Watson. Specifically, we show that for finite p and with T as a conditionally expectation operator, spaces Lp are sequentially complete. Furthermore, we demonstrate that a de La Vall\'e Poussin Theorem does not hold in the general setting of vector lattices.
Keywords
Cite
@article{arxiv.2304.07251,
title = {Uniform Integrability in vector lattices and applications},
author = {Youssef Azouzi},
journal= {arXiv preprint arXiv:2304.07251},
year = {2023}
}