Mean-Square Continuity on Homogeneous Spaces of Compact Groups
  We show that any finite-variance, isotropic random field on a compact group is necessarily mean-square continuous, under standard measurability assumptions. The result extends to isotropic random fields defined on homogeneous spaces where the group acts continuously. 
Domenico Marinucci (DIPMAT), Giovanni Peccati (FSTC)
math.PR