%0 Journal Article
%T Some Properties of Complete Boolean Algebras
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Molkhasi, Ali
%D 2021
%\ 02/13/2021
%V
%N
%P -
%! Some Properties of Complete Boolean Algebras
%K $q^prime$-compactness
%K Strongly algebraically closed algebras
%K Complete Boolean algebras
%R 10.22130/scma.2020.127693.802
%X The main result of this paper is a characterization of the strongly algebraically closed algebras in the lattice of all real-valued continuous functions and the equivalence classes of $lambda$-measurable. We shall provide conditions which strongly algebraically closed algebras carry a strictly positive Maharam submeasure. Particularly, it is proved that if $B$ is a strongly algebraically closed lattice and $(B,, sigma)$ is a Hausdorff space and $B$ satisfies the $G_sigma$ property, then $B$ carries a strictly positive Maharam submeasure.
%U