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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.

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    thank you. I got a solution2012-05-25

1 Answers 1

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recall Fubini’s theorem and apply to couple of function $(f(x|t) ,p(t))$

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    Welcome to MSE. It is not clear how your answer will help solve the problem. Adding in more detail would be helpful.2013-05-05