Relation Between Asymptotic $L_p$-Convergence and Some Classical Modes of Convergence

Abstract

Asymptotic \(L_p\)-convergence, which resembles convergence in \(L_p\), was introduced to address a question in diffusive relaxation. This note aims to compare asymptotic \(L_p\)-convergence with convergence in measure and in weak \(L_p\) spaces. One of the results characterizes convergence in measure on finite measure spaces in terms of asymptotic \(L_p\)-convergence.