Document Type : Research Paper

Author

Department of Mathematics, Faculty of Science, University of Farhangian , Tabriz, Iran.

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.

Keywords

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