Intermediate Value Property for the Assouad Dimension of Measures

IF 0.9 3区数学 Q2 MATHEMATICS

Analysis and Geometry in Metric Spaces Pub Date : 2020-01-01 DOI:10.1515/agms-2020-0106

Ville Suomala

引用次数: 1

Abstract

Abstract Hare, Mendivil, and Zuberman have recently shown that if X ⊂ ℝ is compact and of non-zero Assouad dimension dimA X, then for all s > dimA X, X supports measures with Assouad dimension s. We generalize this result to arbitrary complete metric spaces.

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测度关联维数的中间值性质

Hare、Mendivil和Zuberman最近已经证明，如果X⊂ℝ 是紧致的且具有非零Assouad维数dimA X，则对于所有s>dimA X而言，X支持具有Assouad维度s的测度。我们将此结果推广到任意完全度量空间。

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

Analysis and Geometry in Metric Spaces Mathematics-Geometry and Topology

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Analysis and Geometry in Metric Spaces is an open access electronic journal that publishes cutting-edge research on analytical and geometrical problems in metric spaces and applications. We strive to present a forum where all aspects of these problems can be discussed. AGMS is devoted to the publication of results on these and related topics: Geometric inequalities in metric spaces, Geometric measure theory and variational problems in metric spaces, Analytic and geometric problems in metric measure spaces, probability spaces, and manifolds with density, Analytic and geometric problems in sub-riemannian manifolds, Carnot groups, and pseudo-hermitian manifolds. Geometric control theory, Curvature in metric and length spaces, Geometric group theory, Harmonic Analysis. Potential theory, Mass transportation problems, Quasiconformal and quasiregular mappings. Quasiconformal geometry, PDEs associated to analytic and geometric problems in metric spaces.