Integration on generalized measure spaces
Nous introduisons une notion de multimesure de Radon s-compacte, à valeurs convexes fermées bornées, afin de généraliser et d’unifier des résultats établis, pour des multimesures de Radon à valeurs faiblement compactes, par A. Costé, R. Pallu De La Barrière, K. Siggini, D. S. Thiam. Nous présentons l’intégration par rapport à de telles multimesures de Radon ; et démontrons un théorème de correspondance biunivoque, entre les multimesures faibles monotones s-compactes et les multimesures de Radon...
If C is a capacity on a measurable space, we prove that the restriction of the K-functional to quasicontinuous functions f ∈ QC is equivalent to . We apply this result to identify the interpolation space .
We prove that Poisson measures are invariant under (random) intensity preserving transformations whose finite difference gradient satisfies a cyclic vanishing condition. The proof relies on moment identities of independent interest for adapted and anticipating Poisson stochastic integrals, and is inspired by the method of Üstünel and Zakai (Probab. Theory Related Fields103 (1995) 409–429) on the Wiener space, although the corresponding algebra is more complex than in the Wiener case. The examples...
We consider the set of expanding maps of the circle which have a unique absolutely continuous invariant probability measure whose density is unbounded, and show that this set is dense in the space of expanding maps with the topology. This is in contrast with results for or maps, where the invariant densities can be shown to be continuous.
Let be a non-integer. We consider expansions of the form , where the digits are generated by means of a Borel map defined on . We show existence and uniqueness of a -invariant probability measure, absolutely continuous with respect to , where is the Bernoulli measure on with parameter () and is the normalized Lebesgue measure on . Furthermore, this measure is of the form , where is equivalent to . We prove that the measure of maximal entropy and are mutually singular. In...