Hi all

I have a problem with formal mathematics notation. I guess this is related to probability as well as calculus. Probably to do with conditional expectation too.

I was told that in mathematics, upper case means random variables and lower case means observed variables.

I have two random variables, B and C. They are unknowns.

Then I have a model:

This is kind of limiting C to t to u and B to x to y.

I was told that inside a integral I should write in small case, e.g.

But why?