Document Type : Research Paper
Department of Mathematics, Faculty of Science, University of Farhangian , Tabriz, Iran.
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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