Some remarks on the decomposition of kernels
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- by Arnold Janssen PDF
- Proc. Amer. Math. Soc. 73 (1979), 328-330 Request permission
Abstract:
In a recent paper K. Lange has proved that the decomposition of a stochastic kernel into a continuous and discontinuous part yields kernels again. In the present paper, the author gives a short proof of this theorem and establishes a more general decomposition theorem. Finally, a counter-example shows that in general the Lebesgue decomposition of a kernel does not produce kernels.References
- Lester Dubins and David Freedman, Measurable sets of measures, Pacific J. Math. 14 (1964), 1211–1222. MR 174687
- Arnold Janssen, Über die Meßbarkeit der Mengen der zulässigen und singulären Translationen von Maßen: der Lebesguesche Zerlegungssatz für Kerne, Probability measures on groups (Proc. Fifth Conf., Oberwolfach, 1978) Lecture Notes in Math., vol. 706, Springer, Berlin, 1979, pp. 208–211 (German, with English summary). MR 536986
- Kenneth Lange, Borel sets of probability measures, Pacific J. Math. 48 (1973), 141–161. MR 357723
- Kenneth Lange, Decompositions of substochastic transition functions, Proc. Amer. Math. Soc. 37 (1973), 575–580. MR 314124, DOI 10.1090/S0002-9939-1973-0314124-4
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 73 (1979), 328-330
- MSC: Primary 28A20; Secondary 28C15, 60G05
- DOI: https://doi.org/10.1090/S0002-9939-1979-0518513-X
- MathSciNet review: 518513