有界ae-紧集的太阳性

IF 1.5 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2025-07-29 DOI:10.1134/S1061920825020165

I.G. Tsar’kov

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引用次数: 0

摘要

我们研究有界ae-紧集，对于任意\(\varepsilon>0\)，允许一个\(n\tau\) -连续的\(\varepsilon\) -选择，其中\(\tau\)是测度上收敛的拓扑。在\(L_p\), \(1\leqslant p<\infty\)中，任何这样的集合都显示为太阳。给定一个非空集，证明了对于每个\(\varepsilon>0\)存在一个\(n\tau\) -连续\(\varepsilon\) -选择等价于对于每个\(\varepsilon>0\)存在一个范数-范数连续\(\varepsilon\) -选择。

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Solarity of Boundedly ae-Compact Sets

We study boundedly ae-compact sets admitting, for any \(\varepsilon>0\), an \(n\tau\)-continuous \(\varepsilon\)-selection, where \(\tau\) is the topology of convergence in measure. Any such set in \(L_p\), \(1\leqslant p<\infty\), is shown to be a sun. Given a nonempty set, it is shown that the existence of an \(n\tau\)-continuous \(\varepsilon\)-selection for each \(\varepsilon>0\) is equivalent to existence of a norm-norm continuous \(\varepsilon\)-selection for each \(\varepsilon>0\).

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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.