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arXiv · 1711.09785

On compactness in $L^0$-modules

Asgar Jamneshan·Jose Miguel Zapata
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Abstract

Several results in functional analysis are extended to the setting of $L^0$-modules, where $L^0$ denotes the ring of all measurable functions $x\colon \Omega\to \mathbb{R}$. The focus is on results involving compactness. To this end, a notion of stable compactness is introduced, and it is argued that the conventional notion of compactness does not allow to establish a functional analytic discourse in $L^0$-modules. Several characterizations of stable compactness are discussed, and its importance in applications is highlighted.

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Asgar Jamneshan, Jose Miguel Zapata. 2017-11-27. On compactness in $L^0$-modules. https://arxiv.org/abs/1711.09785

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