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.
"Mean-Square continuity on homogeneous spaces of compact groups." Electron. Commun. Probab. 18 1 - 10, 2013. https://doi.org/10.1214/ECP.v18-2400