递归的一个强Borel-Cantelli引理

IF 0.7 3区数学 Q2 MATHEMATICS

Studia Mathematica Pub Date : 2022-02-15 DOI:10.4064/sm220216-2-7

T. Persson

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引用次数: 3

摘要

摘要考虑一个混合动力系统([0,1]，T， μ)，例如一个Gibbs测度为μ的分段展开区间映射。给定一个非负数的不可和数列(mk)，可以定义rk(x)使得μ(B(x, rk(x)) = mk。证明了对于几乎所有的x, k≤n的个数使得Tk(x)∈Bk(x)近似等于m1 +…+锰。这是递归的一种强Borel-Cantelli引理。结果就是

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A strong Borel–Cantelli lemma for recurrence

ABSTRACT. Consider a mixing dynamical systems ([0, 1], T, μ), for instance a piecewise expanding interval map with a Gibbs measure μ. Given a non-summable sequence (mk) of non-negative numbers, one may define rk(x) such that μ(B(x, rk(x)) = mk. It is proved that for almost all x, the number of k ≤ n such that Tk(x) ∈ Bk(x) is approximately equal to m1 + . . . + mn. This is a sort of strong Borel–Cantelli lemma for recurrence. A consequence is that

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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.