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 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.