University of MaraghehSahand Communications in Mathematical Analysis2322-5807Articles in Press20210213Some Properties of Complete Boolean Algebras24230410.22130/scma.2020.127693.802ENAliMolkhasiDepartment of Mathematics, Faculty of Science, University of Farhangian , Tabriz, Iran.0000-0003-1603-2237Journal Article20200527The 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.