Abstract
For a separating algebra R of subsets of a set X, E a complete Hausdorff non-Archimedean locally convex space and m : R → E a bounded finitely additive measure, we study some of the properties of the integrals with respect to m of scalar-valued functions on X. The concepts of convergence in measure, with respect to m, and of m-measurable functions are introduced and several results concerning these notions are given.
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