A simple proof of a theorem of Chacon
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- by Robert Chen PDF
- Proc. Amer. Math. Soc. 60 (1976), 273-275 Request permission
Abstract:
A short and simple proof of a theorem of Chacon is presented by an application of a maximal inequality. A pointwise convergence theorem and the submartingale convergence theorem follow immediately from the theorem.References
- D. G. Austin, G. A. Edgar, and A. Ionescu Tulcea, Pointwise convergence in terms of expectations, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 30 (1974), 17–26. MR 358945, DOI 10.1007/BF00532860
- J. R. Baxter, Pointwise in terms of weak convergence, Proc. Amer. Math. Soc. 46 (1974), 395–398. MR 380968, DOI 10.1090/S0002-9939-1974-0380968-7
- R. V. Chacon, A “stopped” proof of convergence, Advances in Math. 14 (1974), 365–368. MR 365688, DOI 10.1016/0001-8708(74)90038-3
- Charles W. Lamb, A short proof of the martingale convergence theorem, Proc. Amer. Math. Soc. 38 (1973), 215–217. MR 324770, DOI 10.1090/S0002-9939-1973-0324770-X
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 60 (1976), 273-275
- MSC: Primary 60G40
- DOI: https://doi.org/10.1090/S0002-9939-1976-0420828-8
- MathSciNet review: 0420828