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Measure-theoretic unfriendly colorings

Clinton T. Conley (2014)

Fundamenta Mathematicae

We consider the problem of finding a measurable unfriendly partition of the vertex set of a locally finite Borel graph on standard probability space. After isolating a sufficient condition for the existence of such a partition, we show how it settles the dynamical analog of the problem (up to weak equivalence) for graphs induced by free, measure-preserving actions of groups with designated finite generating set. As a corollary, we obtain the existence of translation-invariant random unfriendly colorings...

Medidas y probabilidades en estructuras ordenadas.

María Congost Iglesias (1981)

Stochastica

This paper is concerned with lattice-group valued measures for which the sygma-additivity is defined by means of the order convergence properties. In the first section we treat the analogues for such order-measures with values in a Dedekind complete lattice-group of the Jordan, Lebesgue and Yosida-Hewitt descompositions. The second section deals with the construction of an integral for functions with respect to an order-measure, both taking their values in a Dedekind sygma-complete lattice-ring....

Mesures canoniques dans le problème classique des moments

Henri Buchwalter, Gilles Cassier (1984)

Annales de l'institut Fourier

Étant donné un problème des moments classique de Hamburger, supposé indéterminé, on montre qu’une mesure μ solution est m -canonique (N. I. Akhiezer, Oliver and Boyd, Edinburgh, 1965, p. 115) si et seulement si l’adhérence H de l’espace des polynômes est exactement de codimension m dans l’espace de Hilbert L 2 ( μ ) . On déduit de là des résultats de perturbation de mesures m -canoniques généralisant ceux de C. Berg et J.-P. R. Christensen (Ann. Inst. Fourier, 31-3 (1981), 99–114), établis pour le cas des...

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