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

Abstract

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