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Decompositions of substochastic transition functions


Author: Kenneth Lange
Journal: Proc. Amer. Math. Soc. 37 (1973), 575-580
MSC: Primary 60J35
DOI: https://doi.org/10.1090/S0002-9939-1973-0314124-4
MathSciNet review: 0314124
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Abstract: Three decompositions of a substochastic transition function are shown to yield substochastic parts. These are the Lebesgue decomposition with respect to a finite measure, the decomposition into completely atomic and continuous parts, and on $ {R^n}$, a decomposition giving a part with continuous distribution function and a part with discontinuous distribution function.


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  • [1] R. B. Ash, Measure, integration, and functional analysis, Academic Press, New York, 1972. MR 0435321 (55:8281)
  • [2] J. L. Doob, Stochastic processes, Wiley, New York; Chapman & Hall, London, 1953. MR 15, 445. MR 0058896 (15:445b)
  • [3] L. Dubins and D. Freedman, Measurable sets of measures, Pacific J. Math. 14 (1964), 1211-1222. MR 30 #4887. MR 0174687 (30:4887)
  • [4] J. M. G. Fell, A Hausdorff topology for the closed subsets of a locally compact non-Hausdorff space, Proc. Amer. Math. Soc. 13 (1962), 472-476. MR 25 #2573. MR 0139135 (25:2573)
  • [5] K. Lange, Borel sets of probability measures, Pacific J. Math. (to appear). MR 0357723 (50:10191)
  • [6] K. R. Parthasarathy, Probability measures on metric spaces, Probability and Math. Statist., no. 3, Academic Press, New York, 1967. MR 37 #2271. MR 0226684 (37:2271)
  • [7] V. S. Varadarajan, Groups of automorphisms of Borel spaces, Trans. Amer. Math. Soc. 109 (1963), 191-220. MR 28 #3139. MR 0159923 (28:3139)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0314124-4
Keywords: Substochastic transition function, space of measures, Lebesgue decomposition, atom, distribution function, Fell topology
Article copyright: © Copyright 1973 American Mathematical Society

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