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Uniformly countably additive families of measures and group invariant measures.

Baltasar Rodríguez-Salinas (1998)

Collectanea Mathematica

The extension of finitely additive measures that are invariant under a group permutations or mappings has already been widely studied. We have dealt with this problem previously from the point of view of Hahn-Banach's theorem and von Neumann's measurable groups theory. In this paper we construct countably additive measures from a close point of view, different to that of Haar's Measure Theory.

Unions et intersections d’espaces L p invariantes par translation ou convolution

Jean-Paul Bertrandias, Christian Datry, Christian Dupuis (1978)

Annales de l'institut Fourier

Étude des propriétés des unions et intersections d’espaces L p ( s ) relatifs à un ensemble S de mesures positives sur un groupe commutatif localement compact lorsque S est invariant par translation ou stable par convolution.Dans des cas particuliers, on retrouve les propriétés d’espaces étudiés par A. Beurling et par B. Koremblium.On étudie aussi les espaces p ( L p ' ) formés des fonctions appartenant localement à L p ' et qui ont un comportement p à l’infini.

Uniqueness of measure extensions in Banach spaces

J. Rodríguez, G. Vera (2006)

Studia Mathematica

Let X be a Banach space, B B X * a norming set and (X,B) the topology on X of pointwise convergence on B. We study the following question: given two (non-negative, countably additive and finite) measures μ₁ and μ₂ on Baire(X,w) which coincide on Baire(X,(X,B)), does it follow that μ₁ = μ₂? It turns out that this is not true in general, although the answer is affirmative provided that both μ₁ and μ₂ are convexly τ-additive (e.g. when X has the Pettis Integral Property). For a Banach space Y not containing...

Upper envelopes of inner premeasures

Heinz König (2000)

Annales de l'institut Fourier

The paper resumes one of the themes initiated in the final sections of the celebrated “Theory of Capacities” of Choquet 1953-54. It aims at comprehensive versions in the spirit of the author’s recent work in measure and integration.

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