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Keywords:
$\sigma $-finite measure space; measure preserving transformation; conservative; ergodic; supremum of ergodic ratios; maximal and reverse maximal inequalities
$\sigma $-finite measure space; measure preserving transformation; conservative; ergodic; supremum of ergodic ratios; maximal and reverse maximal inequalities
Summary:
Using the ratio ergodic theorem for a measure preserving transformation in a $\sigma $-finite measure space we give a straightforward proof of Derriennic's reverse maximal inequality for the supremum of ergodic ratios.
References:
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