I am reading a proof concerning a conditional density where is a sub -algebra generated by random variables . In the proof, they express this conditional density in terms of the probability of being in some infinitesimal interval ds around t. They write:
Intuitively, this makes sense to me, but I'm not really sure how to understand this more rigorously. I know that a conditioal probability given a -algebra is the same as a conditional expectation of an indicator function, but how do we make sense of this equality and the left hand side?
Edit: is the conditional density of event times in a point process given the first n points.