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Displaying similar documents to “Compact sets without converging sequences in the random real model.”

Weakly α-favourable measure spaces

David Fremlin (2000)

Fundamenta Mathematicae

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I discuss the properties of α-favourable and weakly α-favourable measure spaces, with remarks on their relations with other classes.

On exponential convergence to a stationary measure for a class of random dynamical systems

Sergei B. Kuksin (2001)

Journées équations aux dérivées partielles

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For a class of random dynamical systems which describe dissipative nonlinear PDEs perturbed by a bounded random kick-force, I propose a “direct proof” of the uniqueness of the stationary measure and exponential convergence of solutions to this measure, by showing that the transfer-operator, acting in the space of probability measures given the Kantorovich metric, defines a contraction of this space.

A new proof of Kelley's Theorem

S. Ng (1991)

Fundamenta Mathematicae

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Kelley's Theorem is a purely combinatorial characterization of measure algebras. We first apply linear programming to exhibit the duality between measures and this characterization for finite algebras. Then we give a new proof of the Theorem using methods from nonstandard analysis.

Uniformly completely Ramsey sets

Udayan Darji (1993)

Colloquium Mathematicae

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Galvin and Prikry defined completely Ramsey sets and showed that the class of completely Ramsey sets forms a σ-algebra containing open sets. However, they used two definitions of completely Ramsey. We show that they are not equivalent as they remarked. One of these definitions is a more uniform property than the other. We call it the uniformly completely Ramsey property. We show that some of the results of Ellentuck, Silver, Brown and Aniszczyk concerning completely Ramsey sets also...

Quantitative Isoperimetric Inequalities on the Real Line

Yohann de Castro (2011)

Annales mathématiques Blaise Pascal

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In a recent paper A. Cianchi, N. Fusco, F. Maggi, and A. Pratelli have shown that, in the Gauss space, a set of given measure and almost minimal Gauss boundary measure is necessarily close to be a half-space. Using only geometric tools, we extend their result to all symmetric log-concave measures on the real line. We give sharp quantitative isoperimetric inequalities and prove that among sets of given measure and given asymmetry (distance to half line, i.e. distance to sets...