Correlation Approach to Studying Dependent Discrete Probability Spaces

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.