Further specifications of the process
The results of the last two sections are valid if the M. C. is separable and measurable. These two properties do not determine the sample limit functions with probability one. More precisely, given the initial distribution and the standard transition matrix, there are in general different versions of the process which are measurable and separable with the same separability set but in which sample functions corresponding to the same ω are different for a. a. ω.
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