  Let G be a real semi-simple Lie group and H a closed subgroup which admits an
open orbit on the flag manifold of a minimal parabolic subgroup. Let V be a
Harish-Chandra module. A sharp finite bound is given for the dimension of the
space of H-fixed distribution vectors for V and a related subrepresentation
theorem is derived. Extended final version. To appear in Trans. Amer. Math.
Soc.
