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.
Fubini theorem question
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analysis
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0thank you. I got a solution – 2012-05-25
1 Answers
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recall Fubini’s theorem and apply to couple of function $(f(x|t) ,p(t))$
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4Welcome to MSE. It is not clear how your answer will help solve the problem. Adding in more detail would be helpful. – 2013-05-05