Abstract

The well-known problem of the absence of independent events in some discrete probability spaces (finite or countable) is considered. It is proposed to study such spaces using the minimum absolute value of the correlation coefficient of event indicators (in the case of a countable space, the infimum is taken). Examples of probability space with a prime number of equally possible outcomes, a finite space with weights and irrationality, a geometric space with a prime number of outcomes, and a countable space with probabilities given by the sum of three geometric progressions are considered.

中文翻译：

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研究相关离散概率空间的相关方法

摘要

考虑在一些离散概率空间（有限或可数）中不存在独立事件的众所周知的问题。建议使用事件指标相关系数的最小绝对值来研究此类空间（在可数空间的情况下，取下界）。考虑了具有质数等可能结果的概率空间、具有权重和无理性的有限空间、具有质数结果的几何空间以及具有由三个几何级数之和给出的概率的可数空间的示例。