Dropping weak convergence allows the almost-sure limit of normalized convex hulls of centered Gaussians in Banach spaces to be any convex compact set.
Talagrand, Sur l'integrabilit \'e des vecteurs gaussiens
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A counter-example linked to Gaussian convex hulls
Dropping weak convergence allows the almost-sure limit of normalized convex hulls of centered Gaussians in Banach spaces to be any convex compact set.