  A 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.
