# Article

Full entry | PDF   (0.2 MB)
Keywords:
$\sigma$-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:
[1] Derriennic Y.: On the integrability of the supremum of ergodic ratios. Ann. Probability 1 (1973), 338-340. MR 0352404 | Zbl 0263.28015
[2] Ephremidze L.: On the distribution function of the majorant of ergodic means. Studia Math. 103 (1992), 1-15. MR 1184098
[3] Ephremidze L.: A new proof of the ergodic maximal equality. Real Anal. Exchange 29 (2003/04), 409-411. MR 2063082
[4] Krengel U.: Ergodic Theorems. Walter de Gruyter, Berlin, 1985. MR 0797411 | Zbl 0649.47042
[5] Ornstein D.: A remark on the Birkhoff ergodic theorem. Illinois J. Math. 15 (1971), 77-79. MR 0274719 | Zbl 0212.40102
[6] Sato R.: Maximal functions for a semiflow in an infinite measure space. Pacific J. Math. 100 (1982), 437-443. MR 0669336 | Zbl 0519.28010

Partner of