渐近$L_p$收敛与某些经典收敛模式之间的关系

arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-07-09 DOI:arxiv-2407.06830

Nuno J. Alves, Giorgi G. Oniani

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摘要

渐近$L_p$收敛类似于$L_p$收敛，是由（cite{alves2024mode}）中的一个扩散松弛问题引起的。本注释的主要目的是比较渐近$L_p$收敛与在度量空间和弱$L_p$空间中的收敛。所获得的结果之一是用渐近$L_p$收敛来描述无限度量空间的度量收敛。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Relation between asymptotic $L_p$-convergence and some classical modes of convergence

Asymptotic $L_p$-convergence, which resembles convergence in $L_p$, was introduced in \cite{alves2024mode}, motivated by a question in diffusive relaxation. The main purpose of this note is to compare asymptotic $L_p$-convergence with convergence in measure and in weak $L_p$ spaces. One of the results obtained provides a characterization of convergence in measure on finite measure spaces in terms of asymptotic $L_p$-convergence.

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arXiv - MATH - Classical Analysis and ODEs

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