Martingales in a $\sigma$-finite measure space indexed by directed sets
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- Trans. Amer. Math. Soc. 97 (1960), 254-285 Request permission
References
- Erik Sparre Andersen and Børge Jessen, Some limit theorems on set-functions, Danske Vid. Selsk. Mat.-Fys. Medd. 25 (1948), no. 5, 8. MR 28376
- S. Bochner, Partial ordering in the theory of martingales, Ann. of Math. (2) 62 (1955), 162–169. MR 71669, DOI 10.2307/2007106
- Jean Dieudonné, Sur un théorème de Jessen, Fund. Math. 37 (1950), 242–248 (French). MR 43176, DOI 10.4064/fm-37-1-242-248
- J. L. Doob, Stochastic processes, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1953. MR 0058896
- Paul R. Halmos, Measure Theory, D. Van Nostrand Co., Inc., New York, N. Y., 1950. MR 0033869, DOI 10.1007/978-1-4684-9440-2
- Lester L. Helms, Mean convergence of martingales, Trans. Amer. Math. Soc. 87 (1958), 439–446. MR 94841, DOI 10.1090/S0002-9947-1958-0094841-0
- Meyer Jerison, Martingale formulation of ergodic theorems, Proc. Amer. Math. Soc. 10 (1959), 531–539. MR 117782, DOI 10.1090/S0002-9939-1959-0117782-5
- K. Krickeberg, Convergence of martingales with a directed index set, Trans. Amer. Math. Soc. 83 (1956), 313–337. MR 91328, DOI 10.1090/S0002-9947-1956-0091328-4
- Klaus Krickeberg, Stochastische Konvergenz von Semimartingalen, Math. Z. 66 (1957), 470–486 (German). MR 91329, DOI 10.1007/BF01186623 M. Loève, Probability theory, New York, Van Nostrand, 1955.
- Dorothy Maharam, On two theorems of Jessen, Proc. Amer. Math. Soc. 9 (1958), 995–999. MR 105480, DOI 10.1090/S0002-9939-1958-0105480-2
- Shu-Teh Chen Moy, Measure extensions and the martingale convergence theorem, Proc. Amer. Math. Soc. 4 (1953), 902–907. MR 58903, DOI 10.1090/S0002-9939-1953-0058903-7 S. Saks, Theory of the integral, Warszawa-Lwòw, 1937. Reprinted Stechert-Hafner Publishing Company, New York.
- J. L. Snell, Applications of martingale system theorems, Trans. Amer. Math. Soc. 73 (1952), 293–312. MR 50209, DOI 10.1090/S0002-9947-1952-0050209-9
- Kôsaku Yosida and Edwin Hewitt, Finitely additive measures, Trans. Amer. Math. Soc. 72 (1952), 46–66. MR 45194, DOI 10.1090/S0002-9947-1952-0045194-X
Additional Information
- © Copyright 1960 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 97 (1960), 254-285
- MSC: Primary 60.00
- DOI: https://doi.org/10.1090/S0002-9947-1960-0121835-8
- MathSciNet review: 0121835