TITLE: Bayesian Inference in Measure Theory
QUESTION [11 upvotes]: What's the deal. How does this work, or can you point me to some references? I tried $\mu(A|B) = \mu(A \cap B) / \mu(B)$ and got stuck on $\mu(B) = 0$.
Edit: Sorry for being lazy. My background is the basics of measure theory (working on it): measurable spaces, measurable functions, Lebesgue integral, that's about it so far. I haven't yet learned much about measure theory and probability. I am mainly just curious if there is a "formula" for Bayes' rule in measure theory? And interested in anything relevant.
One motivation is we often model a game in economics by have a finite set of states of the world with a prior distribution, then we learn that the true state is in some subset and update based on Bayes rule. I haven't seen how to model this with an infinite state space (I can only think of special cases where it would work).
Thanks!

REPLY [2 votes]: The Bayes formula in measure theory is studied on Nonparametric Bayesian. 
I suggest you to see the slide 11 on 
http://stat.columbia.edu/~porbanz/talks/MLSS12_2.pdf
where it is read that "NPB models do not generally satisfy Bayes’ theorem".