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 | References | Similar Articles | Additional Information

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.

**[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