On p-adic vector measure spaces

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.