Work

Almost Uniform Vs. Pointwise Convergence from a Linear Point of View

Year: 2026

Type: article

Abstract: A review of the state of the art of the comparison between any two different modes of convergence of sequences of measurable functions is carried out with focus on the algebraic structure of the families under analysis. As a complement of the amount of results obtained by several authors, it is proved, among other assertions and under natural assumptions, the existence of large vector subspaces as well as of large algebras contained in the family of the sequences of measurable functions converging to zero pointwise almost everywhere but not almost uniformly, and in the family of the sequences of measurable functions converging to zero almost uniformly but not uniformly almost everywhere.

Source: Mediterranean Journal of Mathematics

DOI: 10.1007/s00009-026-03093-4

Authors: L. Bernal-González, M. C. Calderón-Moreno, P. J. Gerlach-Mena, J. A. Prado-Bassas

Institution: Universidad de Sevilla

Language: English

Topic: Advanced Banach Space Theory

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Universidad de Sevilla, Agencia Estatal de Investigación