# Questions tagged [fubini]

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### If a double integral does not converge absolutely, does that mean the function is discontinuous? [closed]

An assumption of Fubini's theorem is that: $$\displaystyle{\iint_{R} |f(x,y)| \thinspace \mathrm{d} A < \infty}$$ If this assumption is not met, and the integral of the absolute value of the ...
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### Why are we allowed to replace the integral with respect to the product measure $\mu$ with iterated integrals?(2)
My statement for Fubini theorem is: {Let $(X, \mathcal{S}, \mu)$ and $(Y, \mathcal{T}, \lambda)$ be $\sigma$-finite measure spaces. and let $f$ be a $\mathcal{S} \times \mathcal{T}-$measurable ...
### Why are we allowed to replace the integral with respect to the product measure $\mu$ with iterated integrals?
I was reading this question here Fubini's Theorem double integral with sin and $e^{-x}$ but I do not know why are we allowed to replace the integral with respect to the product measure $\mu$ ...