Displaying similar documents to “A bipolar theorem for L + 0 ( Ω , , 𝐏 )

A note on Pólya's theorem.

Dinis Pestana (1984)

Trabajos de Estadística e Investigación Operativa


The class of extended Pólya functions Ω = {φ: φ is a continuous real valued real function, φ(-t) = φ(t) ≤ φ(0) ∈ [0,1], lím φ(t) = c ∈ [0,1] and φ(|t|) is convex} is a convex set. Its extreme points are identified, and using Choquet's theorem it is shown that φ ∈ Ω has an integral representation of the form φ(|t|) = ∫ max{0, 1-|t|y} dG(y), where G is the distribution function of some random variable Y. As on the other hand max{0, 1-|t|y} is the characteristic function...

Mass transport problem and derivation

Nacereddine Belili, Henri Heinich (1999)

Applicationes Mathematicae


A characterization of the transport property is given. New properties for strongly nonatomic probabilities are established. We study the relationship between the nondifferentiability of a real function f and the fact that the probability measure λ f * : = λ ( f * ) - 1 , where f*(x):=(x,f(x)) and λ is the Lebesgue measure, has the transport property.

On Bárány's theorems of Carathéodory and Helly type

Ehrhard Behrends (2000)

Studia Mathematica


The paper begins with a self-contained and short development of Bárány’s theorems of Carathéodory and Helly type in finite-dimensional spaces together with some new variants. In the second half the possible generalizations of these results to arbitrary Banach spaces are investigated. The Carathéodory-Bárány theorem has a counterpart in arbitrary dimensions under suitable uniform compactness or uniform boundedness conditions. The proper generalization of the Helly-Bárány theorem reads...

Convex-compact sets and Banach discs

I. Monterde, Vicente Montesinos (2009)

Czechoslovak Mathematical Journal


Every relatively convex-compact convex subset of a locally convex space is contained in a Banach disc. Moreover, an upper bound for the class of sets which are contained in a Banach disc is presented. If the topological dual E ' of a locally convex space E is the σ ( E ' , E ) -closure of the union of countably many σ ( E ' , E ) -relatively countably compacts sets, then every weakly (relatively) convex-compact set is weakly (relatively) compact.