On integral representation and the Choquet boundary for convolution algebras of measures

We show that the Choquet boundary of a convolution algebra of measures is contained in the set of generalized characters of idempotent modulus. We then give a number of sufficient conditions for Choquet boundary points and determine the Choquet boundary for some examples, including the examples of Hewitt-Kakutani and Simon. Finally we state and prove a theorem of Bochner's type forL-algebras generated by a single measure.