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Applications sommantes et radonifiantes

Patrice Assouad — 1972

Annales de l'institut Fourier

Soient E , F des espaces de Banach L ϕ , L ψ des espaces d’Orlicz, on définit les applications ϕ - ψ sommantes de E dans F . On montre que de telles applications sont ϕ - ψ radonifiantes de E dans σ ( F ' ' , F ' ) . On donne une factorisation caractéristique des applications ϕ - 0 sommantes.

Recouvrements, derivation des mesures et dimensions.

Patrice Assouad;  Thierry Quentin de Gromard — 2006

Revista Matemática Iberoamericana

Let X be a set with a symmetric kernel d (not necessarily a distance). The space (X,d) is said to have the weak (resp. strong) covering property of degree ≤ m [briefly prf(m) (resp. prF(m))], if, for each family B of closed balls of (X,d) with radii in a decreasing sequence (resp. with bounded radii), there is a subfamily, covering the center of each element of B, and of order ≤ m (resp. splitting into m disjoint families). Since Besicovitch, covering...

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