Borel概率测度的一维传质原理及其应用

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2025-05-06 DOI:10.1016/j.aim.2025.110304

Edouard Daviaud

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引用次数: 0

摘要

本文建立了在环境测度有限时有效的量纲传质原理。我们提供了这一结果的两个应用。我们首先研究了与一些自相似的有重叠的IFS相关的动态覆盖，然后给出了Diophantine近似在[0,1]点之间的有理近似的一个应用，在[0,1]点的展开中，有几个数字等于1。

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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A dimensional mass transference principle for Borel probability measures and applications

In this article, we establish a dimensional mass transference principle valid when the ambient measure is finite. We provide two applications of this result. First we study certain dynamical coverings associated with some self-similar IFS with overlaps and then we give an application in Diophantine approximation to rational approximation among points of

[0, 1]

with few digit equal to 1 in their base-3 expansion.

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来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.