A note on invariant measures

• Autorzy: Niemiec P.
• Języki publikacji: EN

Abstrakty

EN

The aim of the paper is to show that if F is a family of continuous transformations of a nonempty compact Hausdorff space Ω, then there is no F-invariant probabilistic regular Borel measures on Ω iff there are φ1..., φp ∈ F (for some p ≥ 2) and a continuous function u: Ω, p ? R such that Σ σ ∈Spu(x&sigma(1),...,x&sigmap = 0 and lim infn?∞1/n Σ n-1/k=0 (u o Φk)9x1,...xp) ≥ 1 for each x1,...xp ∈ Ω, where Φ: Ωp ∋ (x1,...xp) ? (φ1(x1,..., φp(xp)∈ Ωp and Φk is the k-th iterate of Φ. A modified version of this result in case the family F generates an equicontinuous semigroup is proved.

Słowa kluczowe

EN

invariant measures; equicontinuous semigroups; compact spaces

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2011
• Tom: Vol. 31, no. 3
• Strony: 425--431
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Niemiec P.

• Jagiellonian University Institute of Mathematics ul. Łojasiewicza 6, 30-348 Kraków, Poland,

Bibliografia

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