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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Keywords: Stochastic kernels, decomposition theorem, distribution function
Article copyright: © Copyright 1979 American Mathematical Society