Fubini theorem question Let $f$ and $g$ be Lebesgue measurable nonnegative functions on $\mathbb{R}$.  Let $A_y=\{x:f(x) \geq y\}$ Let $F(y)=\int_{A_y} g(x)dx$.  Prove $\int_{-\infty}^\infty f(x)g(x)dx=\int_0^\infty F(y)dy$.  I know this has to do with Fubini's theorem but I cannot prove it.
recall Fubini’s theorem and apply to couple of function $(f(x|t) ,p(t))$
recall Fubini’s theorem and apply to couple of function $(f(x|t) ,p(t))$