On sets not belonging to algebras

Abstract

AbstractLet be a finite sequence of algebras of sets given on a set with more than pairwise disjoint sets not belonging to It was shown in [4] and [5] that in this case Let us consider, instead a finite sequence of algebras It turns out that if for each natural i ≤ l there exist no less than pairwise disjoint sets not belonging to then But if l ≥ 195 and if for each natural i ≤ l there exist no less than pairwise disjoint sets not belonging to then After consideration of finite sequences of algebras, it is natural to consider countable sequences of algebras. We obtained two essentially important theorems on a countable sequence of almost σ-algebras (the concept of almost σ-algebra was introduced in [4]).