my goal will be to motivate why looking at distribution algebras associated to p-adic lie groups is natural in the context of number theory. more specifically i will try to briefly outline their importance in the p-adic langlands program. and then i will give a simple example of an overconvergent distribution algebra of certain kinds of  p-adic groups with an eye towards illuminating techniques used in my work dagger groups and p-adic distribution algebras (joint w/ matthias strauch and claus sorensen).