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

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.

Authors

Publication Details

Journal
Real Analysis Exchange
Published
2024-08-15
DOI
https://doi.org/10.14321/realanalexch.49.2.1720434606
Citations
1
Primary Topic
Approximation Theory and Sequence Spaces
Type
article
Field-Weighted Citation Impact
0.71
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article

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

Nuno J. Alves, Giorgi Oniani
1 citations
Real Analysis Exchange
Approximation Theory and Sequence Spaces
0.71
article

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

Nuno J. Alves, Giorgi Oniani
article en
1 citations

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.

Real Analysis ExchangeVol. 49(2)
Reduced inequalities
Openalex Percentile: Top 27%
Approximation Theory and Sequence Spaces
0.71
DOISourceOpenAlex
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Relation Between Asymptotic $L_p$-Convergence and Some Classical Modes of Convergence — Nuno J. Alves, Giorgi Oniani · Real Analysis Exchange (2024) | TGRS Research Map | TGRS