Borel-Cantelli引理的推广

Remarks on some conditional generalized Borel-Cantelli lemmas

We discuss some conditional generalized Borel-Cantelli lemmas and investigate their quantitative versions following the ideas of Arthan and Oliva (arXiv: 2012.09942).

A Note on the Borel-Cantelli Lemma

In this short note, we discuss the Barndorff-Nielsen lemma, which is a generalization of well-known Borel-Cantelli lemma. Although the result stated in the Barndorff-Nielsen lemma is correct, it does not follow from the argument proposed in the corresponding proof. In this note, we show this and offer an alternative proof of this lemma. We also propose a new generalization of Borel-Cantelli lemma.

Moment estimates in the first Borel-Cantelli Lemma with applications to mean deviation frequencies

We quantify the elementary Borel-Cantelli Lemma by higher moments of the overlap count statistic in terms of the weighted summability of the probabilities. Applications include mean deviation frequencies in the Strong Law and the Law of the Iterated Logarithm.

一个构造性的Borel-Cantelli引理构造具有所需统计特性的轨道

A constructive Borel-Cantelli Lemma. Constructing orbits with required statistical properties

在可计算度量空间和可计算测度的一般背景下，证明了一类构造性Borel-Cantelli引理：给定一个具有有效可和测度的集合序列（在某种程度上是构造性的）$A_{i}$，存在不包含在无穷多个$A_{i}$中的可计算点.因此，我们获得了存在的可计算点遵循\emph{typical statistical behavior}的动力系统（他们满足伯克霍夫定理）的一大类系统，具有可计算的不变测度和一定的“快速”收敛速度的伯克霍夫平均Lipshitz可观。这是适用于一致双曲系统，分段扩张的地图，系统的间隔与一个冷漠的不动点，它直接意味着存在的可计算的数字是正常的任何基地。