A characterization of complete topological vector spaces with applications to spaces of measurable functions

Ansorena, José L.; Marcos, Alejandro

doi:10.2140/involve.2026.19.517

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A characterization of complete topological vector spaces with applications to spaces of measurable functions

José L. Ansorena and Alejandro Marcos

Vol. 19 (2026), No. 3, 517–540

DOI: 10.2140/involve.2026.19.517

Abstract

The aim of this paper is twofold. Firstly, we give easy-to-handle criteria to determine whether a given family of subsets of a vector space is a neighbourhood basis of the origin for a complete vector topology. Then, we apply these criteria to construct quite general complete topological vector spaces of measurable functions.

Keywords

topological vector spaces, local basis, completeness, convergence in measure, Musielak–Orlicz spaces

Mathematical Subject Classification

Primary: 46-01, 46E30

Milestones

Received: 4 December 2024

Revised: 11 February 2025

Accepted: 13 February 2025

Published: 12 June 2026

Communicated by Mohammad Sal Moslehian

Authors

José L. Ansorena
Department of Mathematics and Computer Sciences Universidad de La Rioja Logroño Spain

Alejandro Marcos
Department of Mathematics and Computer Sciences Universidad de La Rioja Logroño Spain

Vol. 19, No. 3, 2026