The ergodic decomposition defined by actions of amenable groups, part II: more about the role played by the ergodic invariant probability measures in the decomposition

• Autorzy: Zaharopol Radu

Identyfikatory

DOI

10.4064/ba210527-11-10

• Języki publikacji: EN

Abstrakty

EN

Our purpose here is to continue the study of the ergodic decomposition for actions defined by amenable groups, started in [R. Zaharopol, Colloq. Math. 165 (2021)]. We consider the set Γ^(w)_αcpie defined in the above-mentioned paper, and we prove that it is Borel measurable and of maximal probability.

Słowa kluczowe

EN

amenable locally compact separable metric group; ergodic decomposition; ergodic measure; invariant measure; tempered Følner sequence

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2021
• Tom: Vol. 69, no. 1
• Strony: 61--68
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Zaharopol Radu

• Radu Zaharopol 2062, Pauline Blvd., Apt. 2B Ann Arbor, MI 48103-5130, USA

Bibliografia

• [1] E. Lindenstrauss, Pointwise theorems for amenable groups, Invent. Math. 146 (2001), 259-295.
• [2] D. T. H. Worm and S. C. Hille, Ergodic decompositions associated to regular Markov operators on Polish spaces, Ergodic Theory Dynam. Systems 31 (2011), 571–597.
• [3] D. Worm, Semigroups on spaces of measures, Ph.D. thesis, Thomas Stieltjes Institute for Mathematics, 2010.
• [4] R. Zaharopol, The ergodic decomposition defined by actions of amenable groups, Colloq. Math. 165 (2021), 285–319.
• [5] R. Zaharopol, An ergodic decomposition defined by transition probabilities, Acta Appl. Math. 104 (2008), 47–81.