I noticed that CET together with monotone-class arguments is commonly used in theory of discrete-time stochastic processes to construct a joint probability measure from finite-dimensional distributions. At the same time, I often see KET being used to construct a joint probability measure from finite-dimensional distributions in continuous time case. As it requires the state space to have some topological properties, it seem to have more restricted applications comparing to those 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.