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Proceedings of the American Mathematical Society

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Generalized balayage and a Radon-Nikodým theorem


Author: D. J. Herbert
Journal: Proc. Amer. Math. Soc. 26 (1970), 165-167
MSC: Primary 60.05
MathSciNet review: 0266260
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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.


References [Enhancements On Off] (What's this?)

  • [1] J. L. Doob, Generalized sweeping-out and probability, J. Functional Analysis 2 (1968), 207–225. MR 0222959
  • [2] 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
  • [3] 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

DOI: https://doi.org/10.1090/S0002-9939-1970-0266260-6
Keywords: Generalized balayage, supermartingales, martingale convergence, lifting, Radon-Nikodym theorem
Article copyright: © Copyright 1970 American Mathematical Society