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arXiv · 2304.07251

Uniform Integrability in vector lattices and applications

Youssef Azouzi
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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.

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Youssef Azouzi. 2023-04-14. Uniform Integrability in vector lattices and applications. https://arxiv.org/abs/2304.07251

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