Mean-Square Continuity on Homogeneous Spaces of Compact Groups

Domenico Marinucci; Giovanni Peccati

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arXiv · 1210.7676

Mean-Square Continuity on Homogeneous Spaces of Compact Groups

Domenico Marinucci·Giovanni Peccati

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Abstract

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.

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Domenico Marinucci, Giovanni Peccati. 2012-10-29. Mean-Square Continuity on Homogeneous Spaces of Compact Groups. https://arxiv.org/abs/1210.7676

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