Ergodic averages and free ℤ2 actions
Buczolich, Zoltán
Fundamenta Mathematicae, Tome 159 (1999), p. 247-254 / Harvested from The Polish Digital Mathematics Library
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If the ergodic transformations S, T generate a free ℤ2 action on a finite non-atomic measure space (X,S,µ) then for any c1,c2∈ℝ there exists a measurable function f on X for which (N+1)-1∑j=0Nf(Sjx)→c1 and (N+1)-1∑j=0Nf(Tjx)→c2µ-almost everywhere as N → ∞. In the special case when S, T are rationally independent rotations of the circle this result answers a question of M. Laczkovich.

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:212391 
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     title = {Ergodic averages and free $$\mathbb{Z}$^2$ actions},
     journal = {Fundamenta Mathematicae},
     volume = {159},
     year = {1999},
     pages = {247-254},
     zbl = {0944.37002},
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Buczolich, Zoltán. Ergodic averages and free $ℤ^2$ actions. Fundamenta Mathematicae, Tome 159 (1999) pp. 247-254. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv160i3p247bwm/

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