Strict topology and perfect measures. (English) Zbl 0711.28002

The authors study several questions related with \(C_ b(X,E)\), the space of bounded continuous functions from a completely regular space X into a normed space over a field K \((=real\) or complex field). In the particular case where \(K=E={\mathbb{R}}\), they consider the topology \(\beta_ p\) [introduced by G. Koumoullis, Ill. J. Math. 26, 466-478 (1982; Zbl 0471.28003)] on \(C_ b(X,{\mathbb{R}})\) and its dual \(M_ p(X)\), the set of all scalar-valued Baire perfect measures on X. Results concerning Mackey and strongly Mackey spaces are proven.
Reviewer: O.T.Alas


28A12 Contents, measures, outer measures, capacities
28A33 Spaces of measures, convergence of measures
46E10 Topological linear spaces of continuous, differentiable or analytic functions
46E27 Spaces of measures
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