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arXiv · 2112.12085

Abstract integration with respect to measures and applications to modular convergence in vector lattice setting

Antonio Boccuto·Anna Rita Sambucini
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Abstract

A "Bochner-type" integral for vector lattice-valued functions with respect to (possibly infinite) vector lattice-valued measures is presented with respect to abstract convergences, satisfying suitable axioms, and some fundamental properties are studied. Moreover, by means of this integral, some convergence results on operators in vector lattice-valued modulars are proved. Some applications are given to moment kernels and to the Brownian motion.

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Antonio Boccuto, Anna Rita Sambucini. 2021-12-22. Abstract integration with respect to measures and applications to modular convergence in vector lattice setting. https://doi.org/10.1007/s00025-022-01776-4

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