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Canonical Banach function spaces generated by Urysohn universal spaces. Measures as Lipschitz maps

Piotr Niemiec (2009)

Studia Mathematica

It is proved (independently of the result of Holmes [Fund. Math. 140 (1992)]) that the dual space of the uniform closure C F L ( r ) of the linear span of the maps x ↦ d(x,a) - d(x,b), where d is the metric of the Urysohn space r of diameter r, is (isometrically if r = +∞) isomorphic to the space L I P ( r ) of equivalence classes of all real-valued Lipschitz maps on r . The space of all signed (real-valued) Borel measures on r is isometrically embedded in the dual space of C F L ( r ) and it is shown that the image of the embedding...

Continuous linear functionals on the space of Borel vector measures

Pola Siwek (2008)

Annales Polonici Mathematici

We study properties of the space ℳ of Borel vector measures on a compact metric space X, taking values in a Banach space E. The space ℳ is equipped with the Fortet-Mourier norm | | · | | and the semivariation norm ||·||(X). The integral introduced by K. Baron and A. Lasota plays the most important role in the paper. Investigating its properties one can prove that in most cases the space ( , | | · | | ) * is contained in but not equal to the space (ℳ,||·||(X))*. We obtain a representation of the continuous functionals on...

Convergenza debole di misure su spazi di funzioni semicontinue

Gianni Dal Maso, Ennio De Giorgi, Luciano Modica (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Given a complete and separable metric space X , we study the weak convergence of sequences of measures defined on the space 𝒮 ( X ) of all real-valued lower semicontinuous functions on X as well as on the space ( X ) of all closed subsets of X .

Convex Corson compacta and Radon measures

Grzegorz Plebanek (2002)

Fundamenta Mathematicae

Assuming the continuum hypothesis, we show that (i) there is a compact convex subset L of Σ ( ω ) , and a probability Radon measure on L which has no separable support; (ii) there is a Corson compact space K, and a convex weak*-compact set M of Radon probability measures on K which has no G δ -points.

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