P-adic Measures and P-adic Spaces of Continuous Functions

Abstract

For $X$ a Hausdorff zero-dimensional topological space and $E$ a Hausdorff  non-Archimedean locally convex space, let $C(X,E)$ (resp. $C_{b}(X,E)$) be  the space of all continuous (resp.  bounded continuous ) $E$-valued functions  on $X$. Some of the properties of the spaces $C(X,E),\ \ C_{b}(X,E)$,  equipped with certain locally convex topologies, are studied. Also, some  complete spaces of measures, on the algebra of all clopen subsets of $X$, are  investigated.