On a theorem of P. S. Muhly

Abstract

The purpose of this paper is to show that if M A {\mathfrak {M}_\mathfrak {A}} is the maximal ideal space of the function algebra induced by a strictly ergodic flow, then almost every point in M A {\mathfrak {M}_\mathfrak {A}} has a unique representing measure which is concentrated on an orbit. This result enables us to extend some theorems of Muhly to a more general setting.