Vol. 69, No. 2, 1977

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Mesures cylindriques, mesures vectorielles et questions de concentration cylindrique

André Goldman

Vol. 69 (1977), No. 2, 385–413

Let E be a locally convex space and mE an E-valued vector measure, absolutely continuous with respect to a scalar measure μ; to each pair (m) we can associate a cylindrical mesure λ on E. It is shown some Radon-Nikodym theorems can be deduced from the properties of the cylindrical concentration of λ. It is shown also that the σ-dentability properties of certain subsets of E are closely related to some particular conditions of cylindrical concentration (these conditions are introduced by A. Badrikian and S. Chevet in the recent book “Mesures cylindriques, espaces de Wiener et fonctions aléatoires gaussiennes”). Finally, we consider the particular case of a measure m which takes its values into the positive cone of a measure space such as Mt(T) (tight measures), Mt(T) (smooth measures), or M(T) (separable measures introduced by Dudley).

Mathematical Subject Classification
Primary: 28A40, 28A40
Received: 13 May 1976
Published: 1 April 1977
André Goldman