Definable convolution and idempotent Keisler measures

We initiate a systematic study of the convolution operation on Keisler measures, generalizing work Newelski in case types. Adapting results Glicksberg, we show that supports definable and finitely satisfiable (or just definable, assuming NIP) measures are nice semigroups, classify idempotent stable groups as invariant type-definable subgroups. establish left-continuity map NIP theories, use it to semigroup is isomorphic particular Ellis this context.