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Proceedings of the American Mathematical Society

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A simple proof of a theorem of Chacon


Author: Robert Chen
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
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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 [Enhancements On Off] (What's this?)

  • [1] D. G. Austin, G. A. Edgar and A. Ionescu Tulcea (1974), Pointwise convergence in terms of expectations, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 30, 17-26. MR 50 #11402. MR 0358945 (50:11402)
  • [2] J. R. Baxter (1974), Pointwise in terms of weak convergence, Proc. Amer. Math. Soc. 46, 395-398. MR 0380968 (52:1865)
  • [3] R. V. Chacon (1974), A ``stopped'' proof of convergence, Advances in Math. 14, 365-368. MR 0365688 (51:1940)
  • [4] C. W. Lamb (1973), A short proof of the martingale convergence theorem, Proc. Amer. Math. Soc. 38, 215-217. MR 48 #3119. MR 0324770 (48:3119)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0420828-8
Keywords: Bounded stopping time, Fatou's lemma, generalized sequence, Lebesgue's dominated convergence theorem, maximal inequality, submartingale convergence theorem
Article copyright: © Copyright 1976 American Mathematical Society

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