Generalized balayage and a Radon-Nikodým theorem
Author:
D. J. Herbert
Journal:
Proc. Amer. Math. Soc. 26 (1970), 165-167
MSC:
Primary 60.05
DOI:
https://doi.org/10.1090/S0002-9939-1970-0266260-6
MathSciNet review:
0266260
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Abstract | References | Similar Articles | Additional Information
Abstract: A simplified proof is given of Doob’s result that a balayage ordered collection of probability measures on a compact Hausdorff space $K$ yields a $K$-valued supermartingale with the measures as marginal distributions. The proof shows further connections with martingale convergence theory.
- J. L. Doob, Generalized sweeping-out and probability, J. Functional Analysis 2 (1968), 207–225. MR 0222959, DOI https://doi.org/10.1016/0022-1236%2868%2990018-9
- Michel Métivier, Martingales à valeurs vectorielles. Application à la dérivation, Symposium on Probability Methods in Analysis (Loutraki, 1966) Springer, Berlin, 1967, pp. 239–255 (French). MR 0220339
- Paul-A. Meyer, Probability and potentials, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1966. MR 0205288
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Additional Information
Keywords:
Generalized balayage,
supermartingales,
martingale convergence,
lifting,
Radon-Nikodym theorem
Article copyright:
© Copyright 1970
American Mathematical Society