Orbital decompositions of invariant distributions on a locally compact zero-dimensional space (Q1067020)

Let G be a locally compact totally disconnected group and X a locally compact zero-dimensional space on which G acts continuously. Linear forms on the space of all compactly supported, locally constant functions on X are called distributions on X. The author studies conditions under which an invariant distribution on X can be decomposed into the orbital ones. The results are applied to the case of the group GL(n,k) (k a non- Archimedean field of characteristic zero) acting on itself via inner automorphisms.