Geodesic
Another proof of Derriennic's reverse maximal inequality for the supremum of ergodic ratios
Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 1, pp. 155-158.

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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.
Classification : 28D05, 47A35
Keywords: $\sigma $-finite measure space; measure preserving transformation; conservative; ergodic; supremum of ergodic ratios; maximal and reverse maximal inequalities 
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Sato, Ryotaro. Another proof of Derriennic's reverse maximal inequality for the supremum of ergodic ratios. Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 1, pp. 155-158. http://geodesic.mathdoc.fr/item/CMUC_2006__47_1_a13/