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.

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

Antonio Boccuto
Membro del Collaboration Group
;
Anna Rita Sambucini
Membro del Collaboration Group
2023

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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1533953
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