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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Some remarks on the decomposition of kernels


Author: Arnold Janssen
Journal: Proc. Amer. Math. Soc. 73 (1979), 328-330
MSC: Primary 28A20; Secondary 28C15, 60G05
MathSciNet review: 518513
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0518513-X
PII: S 0002-9939(1979)0518513-X
Keywords: Stochastic kernels, decomposition theorem, distribution function
Article copyright: © Copyright 1979 American Mathematical Society