Exact $𝓒^{∞}$ covering maps of the circle without (weak) limit measure

• Autorzy: Roland Zweimüller
• Języki publikacji: EN

Abstrakty

EN

We construct $𝓒^{∞}$ maps T on the interval and on the circle which are Lebesgue exact preserving an absolutely continuous infinite measure μ ≪ λ, such that for any probability measure ν ≪ λ the sequence $(n^{-1} ∑_{k=0}^{n-1} ν∘T^{-k})_{n≥1}$ of arithmetical averages of image measures does not converge weakly.

Kategorie tematyczne

• 37E10: Maps of the circle
• 37A40: Nonsingular (and infinite-measure preserving) transformations
• 28D05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2002
• Tom: 93
• Numer: 2
• Strony: 295-302

Daty

wydano

2002

Twórcy

autor

Roland Zweimüller

• Institut für Mathematik, Universität Salzburg, Hellbrunnerstraße 34, A-5020 Salzburg, Austria

Identyfikatory

DOI

10.4064/cm93-2-9