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p -symmetric bi-capacities

Pedro Miranda, Michel Grabisch (2004)

Kybernetika

Bi-capacities have been recently introduced as a natural generalization of capacities (or fuzzy measures) when the underlying scale is bipolar. They allow to build more flexible models in decision making, although their complexity is of order 3 n , instead of 2 n for fuzzy measures. In order to reduce the complexity, the paper proposes the notion of p -symmetric bi- capacities, in the same spirit as for p -symmetric fuzzy measures. The main idea is to partition the set of criteria (or states of nature,...

Pairwise Borel and Baire measures in bispaces

Pratulananda Das, Amar Kumar Banerjee (2005)

Archivum Mathematicum

In this paper we continue the study of the concepts of pairwise Borel and Baire measures in a bispace, recently introduced in [10]. We investigate some of its consequences including the problem of a pairwise regular Borel extension of a pairwise Baire measure.

Partial densities on the group of integers

Harald Niederreiter, Norris Sookoo (2000)

Archivum Mathematicum

Conditions are obtained under which a partial density on the group of integers with the discrete topology can be extended to a density.

Poincaré's recurrence theorem for set-valued dynamical systems

Jean-Pierre Aubin, Hélène Frankowska, Andrzej Lasota (1991)

Annales Polonici Mathematici

 Abstract. The existence theorem of an invariant measure and Poincare's Recurrence Theorem are extended to set-valued dynamical systems with closed graph on a compact metric space.

Pointwise limits for sequences of orbital integrals

Claire Anantharaman-Delaroche (2010)

Colloquium Mathematicae

In 1967, Ross and Stromberg published a theorem about pointwise limits of orbital integrals for the left action of a locally compact group G on (G,ρ), where ρ is the right Haar measure. We study the same kind of problem, but more generally for left actions of G on any measure space (X,μ), which leave the σ-finite measure μ relatively invariant, in the sense that sμ = Δ(s)μ for every s ∈ G, where Δ is the modular function of G. As a consequence, we also obtain a generalization of a theorem of Civin...

Positive vector measures with given marginals

Surjit Singh Khurana (2006)

Czechoslovak Mathematical Journal

Suppose E is an ordered locally convex space, X 1 and X 2 Hausdorff completely regular spaces and Q a uniformly bounded, convex and closed subset of M t + ( X 1 × X 2 , E ) . For i = 1 , 2 , let μ i ∈ M t + ( X i , E ) . Then, under some topological and order conditions on E , necessary and sufficient conditions are established for the existence of an element in Q , having marginals μ 1 and μ 2 .

Processus de Markov et désintégrations régulières

Laurent Schwartz (1977)

Annales de l'institut Fourier

Un théorème classique exprime qu’à partir d’un semi-groupe ( P t ) t ≥ 0 d’opérateurs sur l’espace des fonctions continues tendant vers 0 à l’infini, P s + t = P t , P s ≥ 0 , P t l = 1 , t → P t f continue, P 0 = I , on peut construire un processus markovien “standard”, à trajectoires réglées et continues à droite, quasi-continu à gauche ; l’espace des états E est supposé localement compact à base dénombrable d’ouverts. Nous supposons ici que l’espace des états est seulement universellement mesurable dans un souslinien complètement régulier ; le processus...

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