Exact ∞ covering maps of the circle without (weak) limit measure
Roland Zweimüller
Colloquium Mathematicae, Tome 91 (2002), p. 295-302 / Harvested from The Polish Digital Mathematics Library
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We construct ∞ 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=0n-1ν∘T-k)n≥1 of arithmetical averages of image measures does not converge weakly.

Publié le : 2002-01-01
EUDML-ID : urn:eudml:doc:284686 
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     title = {Exact $^{$\infty$}$ covering maps of the circle without (weak) limit measure},
     journal = {Colloquium Mathematicae},
     volume = {91},
     year = {2002},
     pages = {295-302},
     zbl = {1041.37005},
     language = {en},
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Roland Zweimüller. Exact $^{∞}$ covering maps of the circle without (weak) limit measure. Colloquium Mathematicae, Tome 91 (2002) pp. 295-302. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm93-2-9/