Measure and Integration on Boolean Algebras of Regular Open Subsets in a Topological Space

The regular open subsets of a topological space form Boolean algebra, where the join two sets is interior closure their union. A content finitely additive measure on this or one its subalgebras. We develop theory integration for such contents. then explain relationship between contents, residual charges, and Borel measures. show that can be represented by normal measure, augmented with liminal structure, which specifies how more share common boundary. In particular, locally compact Hausdorff structure Stone-Čech compactification space. also contents measures Stone underlying algebra sets.