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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), 207-255. MR 36 #6009. MR 0222959 (36:6009)
  • [2] M. Metivier, Martingales à valeurs vectorielles: Application à la dérivation, Sympos. on Probability Methods in Analysis (Loutraki, 1966), Springer-Verlag, Berlin and New York, 1967, pp. 239-255. MR 36 #3404. MR 0220339 (36:3404)
  • [3] P. A. Meyer, Probability and potentials, Publ. Inst. Math. Univ. Strasbourg, no. 14, Actualités Sci. Indust., no. 1318, Hermann, Paris, 1966; English transl., Blaisdell, Waltham, Mass., 1966. MR 34 #5118; MR 34 #5119. MR 0205288 (34:5119)

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Keywords: Generalized balayage, supermartingales, martingale convergence, lifting, Radon-Nikodym theorem
Article copyright: © Copyright 1970 American Mathematical Society

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