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.
Der Satz von Choquet-Bishop-de Leeuw für konvexe nicht kompakte Mengen straffer Maße.
Der "Satz von Fubini" in der allgemeinen Integrationstheorie.
Dérivation fonctionnelle abstraite.
Derivation in Orlicz spaces.
Descriptive properties of density preserving autohomeomorphisms of the unit interval
We prove that density preserving homeomorphisms form a Π11-complete subset in the Polish space ℍ of all increasing autohomeomorphisms of unit interval.
Descriptive properties of mappings between nonseparable Luzin spaces
We relate some subsets of the product of nonseparable Luzin (e.g., completely metrizable) spaces to subsets of in a way which allows to deduce descriptive properties of from corresponding theorems on . As consequences we prove a nonseparable version of Kondô’s uniformization theorem and results on sets of points in with particular properties of fibres of a mapping . Using these, we get descriptions of bimeasurable mappings between nonseparable Luzin spaces in terms of fibres.
Descriptive properties of spaces of signed measures
Descriptive set-theoretical properties of an abstract density operator
Let (ℝ) stand for the hyperspace of all nonempty compact sets on the real line and let d ±(x;E) denote the (right- or left-hand) Lebesgue density of a measurable set E ⊂ ℝ at a point x∈ ℝ. In [3] it was proved that is ⊓11-complete. In this paper we define an abstract density operator ⅅ± and we generalize the above result. Some applications are included.
Desintegration and compact measures.
Désintégration d'une mesure
Désintégration d'une mesure non bornée
Désintégration régulière d'une mesure par rapport à une famille de tribus
Désintégrations réguliéres, tribus fortes, et probalités extrémales
Deux essais de généralisation du critère de Grothendieck (compacité faible des ensembles de mesures)
Deux exemples de fonctions non mesurables
Deux mesures spéciales dans l’espace
Diameter of Sets and Measure of Sumsets.
Dichotomies for and spaces
Jachymski showed that the set is either a meager subset of or is equal to . In the paper we generalize this result by considering more general spaces than , namely , the space of all continuous functions which vanish at infinity, and , the space of all continuous bounded functions. Moreover, we replace the meagerness by -porosity.
Die Cantorsche Abbildung ist ein Borel-Isomorphismus.