  The algebraic Sato-Tate conjecture was initially introduced by Serre and then
discussed by Banaszak and Kedlaya. This note shows that the Mumford-Tate
conjecture for an abelian variety A implies the algebraic Sato-Tate conjecture
for A.
  The relevance of this result lies mainly in the fact that the list of known
cases of the Mumford-Tate conjecture was up to now a lot longer than the list
of known cases of the algebraic Sato-Tate conjecture.
