I have mentioned, that CET together with a monotone-class arguments is commonly used in the theory of discrete-time stochastic processes to construct a probability measure out of finite-dimensional distributions. I found it very handy and useful myself, and I guess it extends well to the stochastic fields. At the same time, I often see KET used to construct a probability measure out of finite-dimensional distributions in continuous time case. As it requires the state space to have some topological properties, its application are seems to be less than that of CET.
Updated: more explicit question
I decided to rephrase my questions in a more explicit way: is it true that KET holds without assumptions on the topology of the state space? I have not found the place, where they are used.