×

zbMATH — the first resource for mathematics

Maximal inequalities as necessary conditions for almost everywhere convergence. (English) Zbl 0134.14602

MSC:
60E15 Inequalities; stochastic orderings
60E05 Probability distributions: general theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Alexits, G.: Convergence Problems of Orthogonal Series. New York: Pergamon 1961. · Zbl 0098.27403
[2] Burkholder, D. L.: Successive conditional expectations of an integrable function. Ann. math. Statistics 33, 887-893 (1962). · Zbl 0128.12602 · doi:10.1214/aoms/1177704457
[3] ?, and Y. S. Chow: Iterates of conditional expectation operators. Proc. Amer. math. Soc. 12, 490-495 (1961). · Zbl 0106.33201 · doi:10.1090/S0002-9939-1961-0142144-3
[4] Doob, J. L.: Stochastic Processes. New York: Wiley 1953. · Zbl 0053.26802
[5] Dunford, N., and J. T. Schwartz: Convergence almost everywhere of operator averages. J. Rat. Mech. Analysis 5, 129-178 (1956). · Zbl 0075.12102
[6] ? ?: Linear Operators, I. New York: Interscience 1958. · Zbl 0084.10402
[7] Hope, E.: The general temporally discrete Markoff process. J. Rat. Mech. Analysis 3, 13-45 (1954). · Zbl 0055.36705
[8] Rota, G.-C.: An ?alternierendes Verfahren? for general positive operators. Bull. Amer. Math. Soc. 68, 95-102 (1962). · Zbl 0116.10403 · doi:10.1090/S0002-9904-1962-10737-X
[9] Schwartz, J. T.: Another proof of E. Hopf’s ergodic lemma. Commun. pure appl. Math. 12, 399-401 (1959). · Zbl 0088.32701 · doi:10.1002/cpa.3160120212
[10] Stein, E. M.: On limits of sequences of operators. Ann. of Math. 74, 140-170 (1961). · Zbl 0103.08903 · doi:10.2307/1970308
[11] ?: On the maximal ergodic theorem. Proc. nat. Acad. Sci. USA. 47, 1894-1897 (1961). · Zbl 0182.47102 · doi:10.1073/pnas.47.12.1894
[12] Zygmund, A.: Trigonometric Series, I, II. Cambridge 1959. · Zbl 0085.05601
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.