Ergodic averages and free actions
Zoltán Buczolich (1999)
Fundamenta Mathematicae
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If the ergodic transformations S, T generate a free action on a finite non-atomic measure space (X,S,µ) then for any there exists a measurable function f on X for which and -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.