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

DOI10.1007/S00025-022-01776-4arXiv2112.12085MaRDI QIDQ6386463

Publication date: 22 December 2021

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.

Mathematics Subject Classification ID

Vector-valued set functions, measures and integrals (28B05) Approximation by operators (in particular, by integral operators) (41A35) Other ``topological linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than (mathbb{R}), etc.) (46A19)

This page was built for publication: Abstract integration with respect to measures and applications to modular convergence in vector lattice setting

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6386463)