Finitely subadditive outer measures, finitely superadditive inner measures and their measurable sets.
Finitely-additive, countably-additive and internal probability measures
We discuss two ways to construct standard probability measures, called push-down measures, from internal probability measures. We show that the Wasserstein distance between an internal probability measure and its push-down measure is infinitesimal. As an application to standard probability theory, we show that every finitely-additive Borel probability measure on a separable metric space is a limit of a sequence of countably-additive Borel probability measures in the sense that for all bounded...
Finiteness of Ergodic Unitarily Invariant Measures on Spaces of Infinite Matrices
The main result of this note, Theorem 1.3, is the following: a Borel measure on the space of infinite Hermitian matrices, that is invariant and ergodic under the action of the infinite unitary group and that admits well-defined projections onto the quotient space of “corners" of finite size, must be finite. A similar result, Theorem 1.1, is also established for unitarily invariant measures on the space of all infinite complex matrices. These results imply that the infinite Hua-Pickrell measures...
Finite-tight sets
We introduce two notions of tightness for a set of measurable functions - the finite-tightness and the Jordan finite-tightness with the aim to extend certain compactness results (as biting lemma or Saadoune-Valadier’s theorem of stable compactness) to the unbounded case. These compactness conditions highlight their utility when we look for some alternatives to Rellich-Kondrachov theorem or relaxed lower semicontinuity of multiple integrals. Finite-tightness locates the great growths of a set of...
First class selectors for weakly upper semi-continuous multi-valued maps in Banach spaces.
Fixed points of measure preserving torus homeomorphisms.
Fixed points of semigroups of positive operators in KB-spaces
Flatness of Domains and Doubling Properties of Measures Supported on their Boundary, with Applications to Harmonic Measure.
Flow equivalence, hyperbolic systems and a new zeta function for flows.
Flows in infinite networks
Flows in Networks and Hausdorff Measures Associated. Applications to Fractal Sets in Euclidian Space
Flux moyen d'un courant électrique dans un réseau aléatoire stationnaire de résistances
Fonction convexe d'une mesure et applications
Fonctions continues et séparément additives
Fonctions Généralisées et Analyse Non Standard.
Fonctions mesurables et *-scalairement mesurables, mesures banachiques majorées, martingales banachiques, et propriété de Radon-Nikodym
For almost every tent map, the turning point is typical
Let be the tent map with slope a. Let c be its turning point, and the absolutely continuous invariant probability measure. For an arbitrary, bounded, almost everywhere continuous function g, it is shown that for almost every a, . As a corollary, we deduce that the critical point of a quadratic map is generically not typical for its absolutely continuous invariant probability measure, if it exists.
Foreword
Formes linéaires positives et mesures
Formule(s) de Pesin