We prove an analogue of Topsøe's criterion for relative compactness of a family of probability measures which are regular with respect to a family sets. We consider measures whose values are compact convex sets in a locally convex linear topological space.
We prove necessary and sufficient conditions for the validity of the classical chain rule in the Sobolev space and in the space of functions of bounded variation.
We define the Hake-variational McShane integral of Banach space valued functions defined on an open and bounded subset of -dimensional Euclidean space . It is a “natural” extension of the variational McShane integral (the strong McShane integral) from -dimensional closed non-degenerate intervals to open and bounded subsets of . We will show a theorem that characterizes the Hake-variational McShane integral in terms of the variational McShane integral. This theorem reduces the study of our...
Recently Entov and Polterovich asked if the Grubb measure was the only symplectic topological measure on the torus. Much to our surprise we discovered a whole new class of intrinsic simple topological measures on the torus, many of which were symplectic.
We study the closures of classes of log-concave measures under taking weak limits, linear transformations and tensor products. We investigate which uniform measures on convex bodies can be obtained starting from some class 𝒦. In particular we prove that if one starts from one-dimensional log-concave measures, one obtains no non-trivial uniform mesures on convex bodies.
Nous rassemblons divers résultats sur les nombres normaux et en déduisons de nouveaux résultats.