Geodesic
Exact ${\cal C}^{\infty }$ covering maps of the circle without (weak) limit measure
Roland Zweimüller1
1 Institut für Mathematik Universität Salzburg Hellbrunnerstraße 34 A-5020 Salzburg, Austria
Colloquium Mathematicum, Tome 93 (2002) no. 2, pp. 295-302.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We construct ${\cal C}^{\infty }$ maps $T$ on the interval and on the circle which are Lebesgue exact preserving an absolutely continuous infinite measure $\mu \ll \lambda $, such that for any probability measure $\nu \ll \lambda $ the sequence $(n^{-1}\sum _{k=0}^{n-1}\nu \circ T^{-k})_{n\geq 1}$ of arithmetical averages of image measures does not converge weakly.
DOI : 10.4064/cm93-2-9
Keywords: construct cal infty maps interval circle which lebesgue exact preserving absolutely continuous infinite measure lambda probability measure lambda sequence sum n circ k geq arithmetical averages image measures does converge weakly

Roland Zweimüller 1

1 Institut für Mathematik Universität Salzburg Hellbrunnerstraße 34 A-5020 Salzburg, Austria 
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 without (weak) limit measure},
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Roland Zweimüller. Exact ${\cal C}^{\infty }$ covering maps of the circle
 without (weak) limit measure. Colloquium Mathematicum, Tome 93 (2002) no. 2, pp. 295-302. doi : 10.4064/cm93-2-9. http://geodesic.mathdoc.fr/articles/10.4064/cm93-2-9/

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