## 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