Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces

Ambrosio, Luigi; Figalli, Alessio

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 20 (2011) no. 2, pp. 407-438.

Dans cet article nous étudions la structure de l’ensemble des points avec densité $1/2$ pour les ensemble de périmètre fini dans un espace gaussien infini-dimensionnel. Nous démontrons que, comme dans le cas de dimension finie, la mesure de surface est concentrée sur cet ensemble de points. Ici, la définition de points avec densité $1/2$ est donnée en utilisant le comportement ponctuel du semigroupe de Ornstein-Uhlembeck.

We study points of density $1/2$ of sets of finite perimeter in infinite-dimensional Gaussian spaces and prove that, as in the finite-dimensional theory, the surface measure is concentrated on this class of points. Here density $1/2$ is formulated in terms of the pointwise behaviour of the Ornstein-Uhlembeck semigroup.

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