The sup-completion of a Dedekind complete vector lattice
Functional Analysis
2021-04-29 v1
Abstract
Every Dedekind complete Riesz space X has a unique sup-completion X^{s}, which is a Dedekind complete lattice cone. This paper aims to present a systematic study this cone by extending several known results to general setting, proving new results and, in particular, introducing for elements of X^{s} finite and infinite parts. This enuables us to get a satisfactory abstract formulation of some classical results in the setting of Riesz spaces. We prove, in pareticular, a Riesz space version of Borel-Cantelli Lemma and present some applications to it.29*
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Cite
@article{arxiv.2104.13664,
title = {The sup-completion of a Dedekind complete vector lattice},
author = {Youssef Azouzi and Youssef Nasri},
journal= {arXiv preprint arXiv:2104.13664},
year = {2021}
}
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29 pages