2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65988A compact Lie group G and a faithful complex representation V determine a Sato-Tate measure, defined as the direct image of Haar measure on G with respect to the character of V. We give a necessary and sufficient condition for a Sato-Tate measure to be an isolated point in the set of such measures, regarded as a subset of the space of distributions. In particular we prove that the Sato-Tate measure of a connected and semisimple group with respect to an irreducible representation is an isolated point.11 pagesRepresentation TheoryGroup Theory22E15 (Primary) 11L05, 11T23 (Secondary)text