This is something addressed by probability theory, not CS. While MCMC is easier to explain and understand for discrete spaces, it can also be used for continuou

This is something addressed by probability theory, not CS. While MCMC is easier to explain and understand for discrete spaces, it can also be used for continuous spaces. As a non-mathematician I just think about this as "discretizing at an infinitely high resolution", but of course to an actual mathematician/statistician this is nonsense.