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Some Properties of Complete Boolean Algebras

Journal: Sahand Communications in Mathematical Analysis (Vol.18, No. 2)

Publication Date:

Authors : ;

Page : 63-71

Keywords : $q^prime$-compactness; Strongly algebraically closed algebras; Complete Boolean algebras;

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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.

Last modified: 2021-11-03 14:32:34