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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

##### MSC:
 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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##### References:
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