Some Remarks on the Decomposition of Kernels

Arnold Janssen
1979 Proceedings of the American Mathematical Society  
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 counterexample shows that in general the Lebesgue decomposition of a kernel does not produce kernels.
doi:10.2307/2042356 fatcat:ry2gl7v6qrhcpmizcn3wjkyfb4