Fubini's theorem

Summary

In mathematical analysis, Fubini's theorem is a result that gives conditions under which it is possible to compute a double integral by using an iterated integral, introduced by Guido Fubini in 1907. One may switch the order of integration if the double integral yields a finite answer when the integrand is replaced by its absolute value. , \iint\limits_{X\times Y} f(x,y),\text{d}(x,y) = \int_X\left(\int_Y f(x,y),\text{d}y\right)\text{d}x=\int_Y\left(\int_X f(x,y) , \text{d}x \right) \text{d}y \qquad \text{ if } \qquad \iint\limits_{X\times Y} |f(x,y)|,\text{d}(x,y)

Official source

https://en.wikipedia.org/wiki/Fubini's_theorem

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