- Tytuł:
- A note on invariant measures
- Autorzy:
- Niemiec, P.
- Powiązania:
- https://bibliotekanauki.pl/articles/255767.pdf
- Data publikacji:
- 2011
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
invariant measures
equicontinuous semigroups
compact spaces - Opis:
- 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.
- Źródło:
-
Opuscula Mathematica; 2011, 31, 3; 425-431
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł