Ahlfors正则空间的dvoretzky型定理

IF 0.7 3区 数学 Q2 MATHEMATICS
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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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
Studia Mathematica 数学-数学
CiteScore
1.50
自引率
12.50%
发文量
72
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.
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