The sup-completion of a Dedekind complete vector lattice
Abstract
Every Dedekind complete Riesz space X has a unique sup-completion Xs, 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 Xs 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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