Summary
We give a simple proof of the fact that a Radon gaussian measure on a locally convex vector space is carried by a countable union of metrisable compact sets. We show that a separable centered gaussian process with continuous covariance which is defined on a Polish space X, and is a.e. unbounded on any open set, has a.e. dense trajectories in X × ℝ. These results allow us to show that for any set I, any gaussian measure on ℝI is Τ-smooth.
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Talagrand, M. La Τ-régularité des mesures Gaussiennes. Z. Wahrscheinlichkeitstheorie verw Gebiete 57, 213–221 (1981). https://doi.org/10.1007/BF00535490
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DOI: https://doi.org/10.1007/BF00535490