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

Roland Zweimüller. "Exact $^{∞}$ covering maps of the circle without (weak) limit measure." Colloquium Mathematicae 93.2 (2002): 295-302. <http://eudml.org/doc/284686>.

@article{RolandZweimüller2002,
abstract = {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 $(n^\{-1\} ∑_\{k=0\}^\{n-1\} ν∘T^\{-k\})_\{n≥1\}$ of arithmetical averages of image measures does not converge weakly.},
author = {Roland Zweimüller},
journal = {Colloquium Mathematicae},
keywords = {Perron-Frobenius operator exactness; nonsingular map; weak convergence of measures; quadratic maps},
language = {eng},
number = {2},
pages = {295-302},
title = {Exact $^\{∞\}$ covering maps of the circle without (weak) limit measure},
url = {http://eudml.org/doc/284686},
volume = {93},
year = {2002},
}

TY - JOUR
AU - Roland Zweimüller
TI - Exact $^{∞}$ covering maps of the circle without (weak) limit measure
JO - Colloquium Mathematicae
PY - 2002
VL - 93
IS - 2
SP - 295
EP - 302
AB - 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 $(n^{-1} ∑_{k=0}^{n-1} ν∘T^{-k})_{n≥1}$ of arithmetical averages of image measures does not converge weakly.
LA - eng
KW - Perron-Frobenius operator exactness; nonsingular map; weak convergence of measures; quadratic maps
UR - http://eudml.org/doc/284686
ER -