On systems of independent sets

Abstract

The classical probability that a randomly chosen number from the set {n ∈ N : n ≤ n0} belongs to a set A ⊆ N can be approximated for large number n0 by the asymptotic density of the set A. We say that the events are independent if the probability of their intersection is equal to the product of their probabilities. By analogy we define the independence of sets. We say that the sets are independent if the asymptotic density of their intersection is equal to the product of their asymptotic densities. In the article is described a generalisation of one of the criteria of independence of sets and one interesting case in which sets are not independent