LAUSR

We extend the definition of topological entropy for any (not necessarily continuous) amenable groups acting on a compact space by defining entropy of arbitrary subsets of a product space. We investigate how this new notion of topological entropy for amenable group actions behaves and some of its basic properties; among them are the behavior of the entropy with respect to disjoint union, Cartesian product, and some continuity properties with respect to Vietoris topology. As a special case for $1\leq p\leq \infty $ , the Bowen p-entropy of sets is introduced. It is shown that the notions of generalized topological entropy and Bowen $\infty $ -entropy for compact metric spaces coincide.