Transportation approach to some concentration inequalities in product spaces.
Transportation Cost for Gaussian and Other Product Measures.
Travaux de Krickeberg et de Giorgi sur l'application de la théorie des distributions à l'étude de l'aire des surfaces
Triangulations of closed sets and bases in function spaces.
Trigonometric sums associated with pseudo-measures
Trivial cases for the Kantorovitch problem
Trivial Cases for the Kantorovitch Problem
Let X and Y be two compact spaces endowed with respective measures μ and ν satisfying the condition µ(X) = v(Y). Let c be a continuous function on the product space X x Y. The mass transfer problem consists in determining a measure ξ on X x Y whose marginals coincide with μ and ν, and such that the total cost ∫ ∫ c(x,y)dξ(x,y) be minimized. We first show that if the cost function c is decomposable, i.e., can be represented as the sum of two continuous functions defined on X and Y, respectively,...
Two classes of measures
Two counterexamples concerning Hausdorff dimensions of projections
Two dimensional probabilities with a given conditional structure
A properly measurable set (where are Polish spaces and is the space of Borel probability measures on ) is considered. Given a probability distribution the paper treats the problem of the existence of -valued random vector for which and -almost surely that possesses moreover some other properties such as “ has the maximal possible support” or “’s are extremal...
Two extension theorems. Modular functions on complemented lattices
We prove an extension theorem for modular functions on arbitrary lattices and an extension theorem for measures on orthomodular lattices. The first is used to obtain a representation of modular vector-valued functions defined on complemented lattices by measures on Boolean algebras. With the aid of this representation theorem we transfer control measure theorems, Vitali-Hahn-Saks and Nikodým theorems and the Liapunoff theorem about the range of measures to the setting of modular functions on complemented...
Two generalizations of Komlós' theorem with lower closure-type applications.
Two ideals connected with strong right upper porosity at a point
Let be the set of upper strongly porous at subsets of and let be the intersection of maximal ideals . Some characteristic properties of sets are obtained. We also find a characteristic property of the intersection of all maximal ideals contained in a given set which is closed under subsets. It is shown that the ideal generated by the so-called completely strongly porous at subsets of is a proper subideal of Earlier, completely strongly porous sets and some of their properties were...
Two point sets with additional properties
A subset of the plane is called a two point set if it intersects any line in exactly two points. We give constructions of two point sets possessing some additional properties. Among these properties we consider: being a Hamel base, belonging to some -ideal, being (completely) nonmeasurable with respect to different -ideals, being a -covering. We also give examples of properties that are not satisfied by any two point set: being Luzin, Sierpiński and Bernstein set. We also consider natural generalizations...
Two Problems of Measurability Concerning Convex Sets in Euclidean Spaces.
Two problems on doubling measures.
Doubling measures appear in relation to quasiconformal mappings of the unit disk of the complex plane onto itself. Each such map determines a homeomorphism of the unit circle on itself, and the problem arises, which mappings f can occur as boundary mappings?
Two results for monocompact measures.
Two Selection Theorems
Two theorems on measurable sets and sets having the Baire property
Two theorems on the Scorza Dragoni property for multifunctions
We point out two theorems on the Scorza Dragoni property for multifunctions. As an application, in particular, we improve a Carathéodory selection theorem by A. Cellina [4], by removing a compactness assumption.