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Teoría ergódica y simetrización.

Francesc Bofill (1982)

Stochastica

We study the relations between simetrization by a limiting process of probabilities and functions defined on a metric compacy product space and their ergodic properties.

The Geometry of Model Spaces for Probability-Preserving Actions of Sofic Groups

Tim Austin (2016)

Analysis and Geometry in Metric Spaces

Bowen’s notion of sofic entropy is a powerful invariant for classifying probability-preserving actions of sofic groups. It can be defined in terms of the covering numbers of certain metric spaces associated to such an action, the ‘model spaces’. The metric geometry of these model spaces can exhibit various interesting features, some of which provide other invariants of the action. This paper explores an approximate connectedness property of the model spaces, and uses it give a new proof that certain...

The Lévy continuity theorem for nuclear groups

W. Banaszczyk (1999)

Studia Mathematica

Let G be an abelian topological group. The Lévy continuity theorem says that if G is an LCA group, then it has the following property (PL) a sequence of Radon probability measures on G is weakly convergent to a Radon probability measure μ if and only if the corresponding sequence of Fourier transforms is pointwise convergent to the Fourier transform of μ. Boulicaut [Bo] proved that every nuclear locally convex space G has the property (PL). In this paper we prove that the property (PL) is inherited...

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