Let E be a locally convex
space and m;Σ → E an E-valued vector measure, absolutely continuous
with respect to a scalar measure μ; to each pair (m,μ) 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).
