Dropping weak convergence allows the almost-sure limit of normalized convex hulls of centered Gaussians in Banach spaces to be any convex compact set.
and Ylvisaker D., Strong law for the maxima of stationary Gaussian processes, Ann.Probab
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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.