Prodistributions
Product decomposition of idempotent measures on compact semigroups
Product measurability and Scorza-Dragoni's type property
Product of vector measures on topological spaces
For , let be completely regular Hausdorff spaces, quasi-complete locally convex spaces, , the completion of the their injective tensor product, the spaces of all bounded, scalar-valued continuous functions on , and -valued Baire measures on . Under certain...
Products of completion regular measures
We investigate the products of topological measure spaces, discussing conditions under which all open sets will be measurable for the simple completed product measure, and under which the product of completion regular measures will be completion regular. In passing, we describe a new class of spaces on which all completion regular Borel probability measures are τ-additive, and which have other interesting properties.
Projective limits of perfect measure spaces
Projective limits of vector measures.
A necessary and sufficient condition for the existence of the projective limit of measures with values in a locally convex space is given. A similar theorem for measures with values in different locally convex spaces (under certain conditions) is given too (in this case, the projective limit is valued in the projective limit of these spaces). Finally, a result about the projective limit of vector measures is stated.
Properties of the class of measure separable compact spaces
We investigate properties of the class of compact spaces on which every regular Borel measure is separable. This class will be referred to as MS. We discuss some closure properties of MS, and show that some simply defined compact spaces, such as compact ordered spaces or compact scattered spaces, are in MS. Most of the basic theory for regular measures is true just in ZFC. On the other hand, the existence of a compact ordered scattered space which carries a non-separable (non-regular) Borel measure...
Properties of time-dependent statistical solutions of the three-dimensional Navier-Stokes equations
This work is devoted to the concept of statistical solution of the Navier-Stokes equations, proposed as a rigorous mathematical object to address the fundamental concept of ensemble average used in the study of the conventional theory of fully developed turbulence. Two types of statistical solutions have been proposed in the 1970’s, one by Foias and Prodi and the other one by Vishik and Fursikov. In this article, a new, intermediate type of statistical solution is introduced and studied. This solution...
Propriété de trace en dimension infinie d'espaces du type Sobolev
Proprites de Radon-Nikodym pour les cones positifs de mesures.
Pushing down Loeb measures.