Ahlfors正则空间的dvoretzky型定理

IF 0.7 3区数学 Q2 MATHEMATICS

Studia Mathematica Pub Date : 2021-06-22 DOI:10.4064/sm210629-2-2

M. Mendel

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引用次数: 1

摘要

．证明了对于任意0 < β < α，任何有界Ahlfors α -正则空间都包含一个β -正则紧子集，该子集将biLipschitzly嵌入到畸变不超过O (α/ (α - β))的超尺度中。当β→α时，畸变的界是渐近紧的。证明中使用的主要工具是超度量骨架定理的正则形式。

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Dvoretzky-type theorem for Ahlfors regular spaces

. It is proved that for any 0 < β < α , any bounded Ahlfors α -regular space contains a β -regular compact subset that embeds biLipschitzly in an ultrametric with distortion at most O ( α/ ( α − β )). The bound on the distortion is asymptotically tight when β → α . The main tool used in the proof is a regular form of the ultrametric skeleton theorem.

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来源期刊

Studia Mathematica 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

5 months

期刊介绍： The journal publishes original papers in English, French, German and Russian, mainly in functional analysis, abstract methods of mathematical analysis and probability theory.