Another proof of Derriennic's reverse maximal inequality for the supremum of ergodic ratios

Ryotaro Sato

Commentationes Mathematicae Universitatis Carolinae (2006)

  • Volume: 47, Issue: 1, page 155-158
  • ISSN: 0010-2628

Abstract

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Using the ratio ergodic theorem for a measure preserving transformation in a σ -finite measure space we give a straightforward proof of Derriennic’s reverse maximal inequality for the supremum of ergodic ratios.

How to cite

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Sato, Ryotaro. "Another proof of Derriennic's reverse maximal inequality for the supremum of ergodic ratios." Commentationes Mathematicae Universitatis Carolinae 47.1 (2006): 155-158. <http://eudml.org/doc/249838>.

@article{Sato2006,
abstract = {Using the ratio ergodic theorem for a measure preserving transformation in a $\sigma $-finite measure space we give a straightforward proof of Derriennic’s reverse maximal inequality for the supremum of ergodic ratios.},
author = {Sato, Ryotaro},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\sigma $-finite measure space; measure preserving transformation; conservative; ergodic; supremum of ergodic ratios; maximal and reverse maximal inequalities; -finite measure space; measure preserving transformation; conservative},
language = {eng},
number = {1},
pages = {155-158},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Another proof of Derriennic's reverse maximal inequality for the supremum of ergodic ratios},
url = {http://eudml.org/doc/249838},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Sato, Ryotaro
TI - Another proof of Derriennic's reverse maximal inequality for the supremum of ergodic ratios
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 1
SP - 155
EP - 158
AB - 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.
LA - eng
KW - $\sigma $-finite measure space; measure preserving transformation; conservative; ergodic; supremum of ergodic ratios; maximal and reverse maximal inequalities; -finite measure space; measure preserving transformation; conservative
UR - http://eudml.org/doc/249838
ER -

References

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  1. Derriennic Y., On the integrability of the supremum of ergodic ratios, Ann. Probability 1 (1973), 338-340. (1973) Zbl0263.28015MR0352404
  2. Ephremidze L., On the distribution function of the majorant of ergodic means, Studia Math. 103 (1992), 1-15. (1992) MR1184098
  3. Ephremidze L., A new proof of the ergodic maximal equality, Real Anal. Exchange 29 (2003/04), 409-411. (2003/04) MR2063082
  4. Krengel U., Ergodic Theorems, Walter de Gruyter, Berlin, 1985. Zbl0649.47042MR0797411
  5. Ornstein D., A remark on the Birkhoff ergodic theorem, Illinois J. Math. 15 (1971), 77-79. (1971) Zbl0212.40102MR0274719
  6. Sato R., Maximal functions for a semiflow in an infinite measure space, Pacific J. Math. 100 (1982), 437-443. (1982) Zbl0519.28010MR0669336

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