Pointwise doubling indices of uniform Bernoulli measures on Bedford-McMullen carpets

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-08-20 DOI:10.1016/j.topol.2025.109549

Hui Rao, Yan-Li Xu, Yuan Zhang

引用次数: 0

Abstract

Doubling measures were introduced by Beurling and Ahlfors in 1956 and they have since become a basic concept in analysis on metric spaces. In this paper, for a measure which is not doubling, we introduce a notion of pointwise doubling index, and calculate the pointwise doubling indices of uniform Bernoulli measures on Bedford-McMullen carpets. As an application, we obtain several new Lipschitz invariants of Bedford-McMullen carpets.

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贝德福德-麦克马伦地毯上均匀伯努利测度的逐点加倍指数

双重测度是由Beurling和Ahlfors于1956年提出的，它已经成为度量空间分析中的一个基本概念。本文针对非加倍测度，引入了逐点加倍指数的概念，并计算了贝德福德-麦克马伦地毯上均匀伯努利测度的逐点加倍指数。作为应用，我们得到了贝德福德-麦克马伦地毯的几个新的Lipschitz不变量。

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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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.