Published online by Cambridge University Press: 12 March 2014
Let 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]).