Decompositions of set functions
Dedekind extension of measures with values in vector lattices.
Definability of small puncture sets
We characterize the class of definable families of countable sets for which there is a single countable definable set intersecting every element of the family.
Definable hereditary families in the projective hierarchy
We show that if ℱ is a hereditary family of subsets of satisfying certain definable conditions, then the reals are precisely the reals α such that . This generalizes the results for measure and category. Appropriate generalization to the higher levels of the projective hierarchy is obtained under Projective Determinacy. Application of this result to the -encodable reals is also shown.
Définition axiomatique de la mesure de Hausdorff
Dense sums
Denseness and Borel complexity of some sets of vector measures
Let ν be a positive measure on a σ-algebra Σ of subsets of some set and let X be a Banach space. Denote by ca(Σ,X) the Banach space of X-valued measures on Σ, equipped with the uniform norm, and by ca(Σ,ν,X) its closed subspace consisting of those measures which vanish at every ν-null set. We are concerned with the subsets and of ca(Σ,X) defined by the conditions |φ| = ν and |φ| ≥ ν, respectively, where |φ| stands for the variation of φ ∈ ca(Σ,X). We establish necessary and sufficient conditions...
Densité des orbites des trajectoires browniennes sous l’action de la transformation de Lévy
Let Tbe a measurable transformation of a probability space , preserving the measureπ. Let X be a random variable with law π. Call K(⋅, ⋅) a regular version of the conditional law of X given T(X). Fix . We first prove that ifB is reachable from π-almost every point for a Markov chain of kernel K, then the T-orbit of π-almost every point X visits B. We then apply this result to the Lévy transform, which transforms the Brownian motion W into the Brownian motion |W| − L, where L is the local time...
Densities of self-similar measures on the line.
Density covers
Density in the space of topological measures
Topological measures (formerly "quasi-measures") are set functions that generalize measures and correspond to certain non-linear functionals on the space of continuous functions. The goal of this paper is to consider relationships between various families of topological measures on a given space. In particular, we prove density theorems involving classes of simple, representable, extreme topological measures and measures, hence giving a way of approximating various topological measures by members...
Density of a family of linear varietes
The measurability of the family, made up of the family of plane pairs and the family of lines in -dimensional space , is stated and its density is given.
Density theorems for measurable transformations
Density theorems for measurable transformations
Density-preserving homeomorphisms
Der Satz von Choquet-Bishop-de Leeuw für konvexe nicht kompakte Mengen straffer Maße.
Der Satz von Dunford-Pettis und die Darstellung von Massen mit Werten in lokalkonvexen Räumen.
Der "Satz von Fubini" in der allgemeinen Integrationstheorie.
Derivability, variation and range of a vector measure
We prove that the range of a vector measure determines the σ-finiteness of its variation and the derivability of the measure. Let F and G be two countably additive measures with values in a Banach space such that the closed convex hull of the range of F is a translate of the closed convex hull of the range of G; then F has a σ-finite variation if and only if G does, and F has a Bochner derivative with respect to its variation if and only if G does. This complements a result of [Ro] where we proved...
Derivación de medidas e integración vectorial bilineal.