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Semicontinuous integrands as jointly measurable maps

Oriol Carbonell-Nicolau (2014)

Commentationes Mathematicae Universitatis Carolinae

Suppose that ( X , 𝒜 ) is a measurable space and Y is a metrizable, Souslin space. Let 𝒜 u denote the universal completion of 𝒜 . For x X , let f ̲ ( x , · ) be the lower semicontinuous hull of f ( x , · ) . If f : X × Y ¯ is ( 𝒜 u ( Y ) , ( ¯ ) ) -measurable, then f ̲ is ( 𝒜 u ( Y ) , ( ¯ ) ) -measurable.

Semi-contractions des espaces localement compacts et cas des variétés complexes

Jean-Jacques Loeb (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

En nous inspirant d’articles de Beardon, nous donnons des résultats concernant les points fixes et les orbites d’auto-applications contractantes et semi-contractantes des espaces connexes localement compacts. Des résultats plus précis sont obtenus dans le cas des variétés complexes Kobayashi hyperboliques.

Semiconvex compacta

Oleh R. Nykyforchyn (1997)

Commentationes Mathematicae Universitatis Carolinae

We define and investigate a generalization of the notion of convex compacta. Namely, for semiconvex combination in a semiconvex compactum we allow the existence of non-trivial loops connecting a point with itself. It is proved that any semiconvex compactum contains two non-empty convex compacta, the center and the weak center. The center is the largest compactum such that semiconvex combination induces a convex structure on it. The convex structure on the weak center does not necessarily coincide...

Semigroup actions on tori and stationary measures on projective spaces

Yves Guivarc'h, Roman Urban (2005)

Studia Mathematica

Let Γ be a subsemigroup of G = GL(d,ℝ), d > 1. We assume that the action of Γ on d is strongly irreducible and that Γ contains a proximal and quasi-expanding element. We describe contraction properties of the dynamics of Γ on d at infinity. This amounts to the consideration of the action of Γ on some compact homogeneous spaces of G, which are extensions of the projective space d - 1 . In the case where Γ is a subsemigroup of GL(d,ℝ) ∩ M(d,ℤ) and Γ has the above properties, we deduce that the Γ-orbits...

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