some properties of complete boolean algebras

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 λ-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, σ) is a hausdorff space and b satisfies the g_σ property, then b carries a strictly positive maharam submeasure.