 A distribution on a group "G" or its Lie algebra is called invariant if it is invariant under conjugation by "G".A distribution on a group "G" or its Lie algebra is called an eigendistribution if it is an eigenvector of the center of the universal enveloping algebra of "G" (identified with the left and right invariant differential operators of "G".Harish-Chandra's regularity theorem states that any invariant eigendistribution on a semisimple group or Lie algebra is a locally integrable function.