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BrownianMotion.Gaussian.Fernique

Gaussian distributions in Banach spaces: Fernique's theorem #

Fernique's theorem: for a Gaussian measure, there exists C > 0 such that the function x ↦ exp (C * ‖x‖ ^ 2) is integrable.

A Gaussian measure has moments of all orders. That is, the identity is in Lp for all finite p.