I have a measure that is supported on . What we are given is that, if we fix the first component , then is a probability measure. Formally (maybe it should integrate to or similar, I cannot define this very well):
I find it very hard to understand this tuple-indexing notation. My question is the following: What kind of assumptions do we need to have a result similar to:
I just think that since for any fixed the measure integrates to 1 (on the second dimension -- apologies for my poor terminology), then integrating over all should also give simply an 'iterated integral' where we first integrate wrt for a fixed , which will integrate to 1 , and then integrate over . But of course, we cannot define
where in the red parts I make an abuse of integartion rules.