Borel measure extensions of measures defined on sub-\(\sigma\)-algebras (Q1977156)

In this paper the authors present a number of new results concerning extension of charges (finitely additive) and measures (countable additive). The novelty of the paper rests on the judicious use of non-standard techniques related to the Loeb measure construction. One of the main theorems is the following: Assume that \(X\) is a \(K\)-analytic topological space (a natural generalization of a Polish space and compact spaces) and that \(A\) is a countably-generated algebra of closed \(G_\delta\)-sets. Then every finite measure on \(A\) has a Radon extension to the Borel sets of \(X\).