In Lecture Note 7, Proof of Result 1 (Factorization Theorem), the last set of equations has
`f_X(x) * f_Y(y) = g(x) h(y) int_x g(x) dx int_y h(y) dx = ...`
The last `dx` should be `dy`:
`f_X(x) * f_Y(y) = g(x) h(y) int_x g(x) dx int_y h(y) dy = ...`
I've corrected this in the PDF version posted on the course web page. Thanks to Brendan for pointing this out.