Some Properties of Complete Boolean Algebras
Journal: Sahand Communications in Mathematical Analysis (Vol.18, No. 2)Publication Date: 2021-05-01
Authors : Ali Molkhasi;
Page : 63-71
Keywords : $q^prime$-compactness; Strongly algebraically closed algebras; Complete Boolean algebras;
Abstract
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.
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Last modified: 2021-11-03 14:32:34