测度的点维和谱

Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-10-01 DOI:10.1016/S0764-4442(01)02043-2

Jean-René Chazottes , Benoît Saussol

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引用次数: 8

摘要

对于一般的carath - psin结构，给出了与Borel概率测度相关的下点维数的新定义。然后，我们证明了该测度的谱与低点维的本质上一致。我们提供了一个来自动力系统的例子。

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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On pointwise dimensions and spectra of measures

We give a new definition of the lower pointwise dimension associated with a Borel probability measure with respect to a general Carathéodory–Pesin structure. Then we show that the spectrum of the measure coincides with the essential supremum of the lower pointwise dimension. We provide an example coming from dynamical systems.

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Comptes Rendus de l'Académie des Sciences - Series I - Mathematics

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