The Converse of the Dominated Ergodic Theorem in Hurewicz Setting
Canadian mathematical bulletin, Tome 34 (1991) no. 3, pp. 405-411

Voir la notice de l'article provenant de la source Cambridge University Press

The converse of the dominated ergodic theorem in infinite measure spaces is extended to non-singular transformations, i.e. transformations that only preserve the measure of null sets. An inverse weak maximal inequality is given and then applied to obtain related results in Orlicz spaces.
DOI : 10.4153/CMB-1991-065-0
Mots-clés : 28D99, 47A35
Szabó, László I. The Converse of the Dominated Ergodic Theorem in Hurewicz Setting. Canadian mathematical bulletin, Tome 34 (1991) no. 3, pp. 405-411. doi: 10.4153/CMB-1991-065-0
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[1] 1. Akcoglu, M. A. and Sucheston, L., On uniform monotonicity of norms and ergodic theorems in function spaces, Supplemento ai Rendiconti del Circolo Matematico di Palermo 8 (1985), 325–335. Google Scholar

[2] 2. Derriennic, Y., On The Integrability of The Supremum of Ergodic Ratios, Ann. Prob. 1 (1973), 338–340. Google Scholar

[3] 3. A, G. Edgar and Sucheston, L., On Maximal Inequalities in Orlicz spaces, Contemporary Mathematics 94 (1989), 113–129. Google Scholar

[4] 4. Fava, N. A., Weak inequalities for product operators, Studia Math. 42 (1972), 271–288. Google Scholar

[5] 5. Frangos, N. and Sucheston, L., On multiparameter ergodic and martingale theorems in infinite measure spaces, Probab. Th. Rel. Fields 71 (1986), 477–490. Google Scholar

[6] 6. Hurewicz, W., Ergodic Theorem without Invariant Measure, Ann. Math. 45 (1944), 192–206. Google Scholar

[7] 7. Krengel, U., Ergodic Theorems. De Gruyter Studies in Mathematics 6(1985). Google Scholar

[8] 8. Ornstein, D. S., A remark on the Birkhoff ergodic theorem, Illinois J. Math 15 (1971), 77–79. Google Scholar

[9] 9. Stein, E. M., Note on the class LlogL, Studia Math 32 (1969), 305–310. Google Scholar

[10] 10. Wiener, Norbert, The ergodic theorem, Duke Math. J. 5 (1939), 1–18. Google Scholar

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