MEASURE THEORY OF COMPLETE BOOLEAN ALGEBRAS

Metric Boolean algebras and constructive measure theory

Complete Ccc Boolean Algebras

Let B be a complete ccc Boolean algebra and let τs be the topology on B induced by the algebraic convergence of sequences in B. 1. Either there exists a Maharam submeasure on B or every nonempty open set in (B, τs) is topologically dense. 2. It is consistent that every weakly distributive complete ccc Boolean algebra carries a strictly positive Maharam submeasure. 3. The topological space (B, τ...

Complete Quotient Boolean Algebras

For I a proper, countably complete ideal on P(X) for some set X , can the quotient Boolean algebra P(X)/I be complete? This question was raised by Sikorski [Si] in 1949. By a simple projection argument as for measurable cardinals, it can be assumed that X is an uncountable cardinal κ, and that I is a κ-complete ideal on P(κ) containing all singletons. In this paper we provide consequences from ...

Simple Complete Boolean Algebras

For every regular cardinal κ there exists a simple complete Boolean algebra with κ generators.

Contributions to the Theory of Weakly Distributive Complete Boolean Algebras

We investigate complete Boolean algebras that carry a continuous submeasure.