Strict topology and perfect measures. (English) Zbl 0711.28002

Khurana, Surjit Singh; Vielma, Jorge E.

Czech. Math. J. 40(115), No. 1, 1-7 (1990).

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

Keywords:

strict topology; space of bounded continuous functions; scalar-valued Baire perfect measures; Mackey spaces

Citations:

Zbl 0479.28006; Zbl 0471.28003

References:

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