Abstract martingales in Banach spaces

Uhl, J. J.

doi:10.1090/S0002-9939-1971-0283595-2

Abstract martingales in Banach spaces
HTML articles powered by AMS MathViewer

by J. J. Uhl

Proc. Amer. Math. Soc. 28 (1971), 191-194

DOI: https://doi.org/10.1090/S0002-9939-1971-0283595-2

PDF | Request permission

Abstract:

The concept of martingale is generalized from probability theory to the setting of Banach spaces. Convergent martingales are characterized. An application to a Radon-Nikodym theorem for vector measures is given.

References

John Y. Barry, On the convergence of ordered sets of projections, Proc. Amer. Math. Soc. 5 (1954), 313–314. MR 0062340, DOI 10.1090/S0002-9939-1954-0062340-X
S. D. Chatterji, A note on the convergence of Banach-space valued martingales, Math. Ann. 153 (1964), 142–149. MR 161376, DOI 10.1007/BF01361182
Ralph DeMarr, A martingale convergence theorem in vector lattices, Canadian J. Math. 18 (1966), 424–432. MR 189097, DOI 10.4153/CJM-1966-045-x
Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
J. L. Doob, Stochastic processes, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1953. MR 0058896
John L. Kelley, General topology, D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. MR 0070144
Ulf Rønnow, On integral representation of vector valued measures, Math. Scand. 21 (1967), 45–53 (1968). MR 243030, DOI 10.7146/math.scand.a-10843
Frank S. Scalora, Abstract martingale convergence theorems, Pacific J. Math. 11 (1961), 347–374. MR 123356