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Bimeasures on topological spaces. (English) Zbl 0587.28009

Let X, Y be completely regular spaces, \(C^ b(X)\) the space of bounded real continuous functions on X, B(X) the algebra generated by the zero subsets of X and \(\Omega =B(X)\times B(Y).\) We examine the relationship between continuous bilinear maps on \(C^ b(X)\times C^ b(Y)\) and the bimeasures on \(\Omega\) which are of bounded semivariation. We also look at an analogous problem for vector-valued bilinear maps on \(C^ b(X)\times C^ b(Y).\)

MSC:

28C15 Set functions and measures on topological spaces (regularity of measures, etc.)
54C40 Algebraic properties of function spaces in general topology
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