Fubini‘s theorem

In mathematical analysis Fubini’s theorem, introduced by Guido Fubini in 1907, is a result that gives conditions under which it is possible to compute a double integral by using an iterated integral. One may switch the order of integration if the double integral yields a finite answer when the integrand is replaced by its absolute value.

As a consequence, it allows the order of integration to be changed in certain iterated integrals. Fubini’s theorem implies that two iterated integrals are equal to the corresponding double integral across its integrands. Tonelli’s theorem, introduced by Leonida Tonelli in 1909, is similar, but applies to a non-negative measurable function rather than one integrable over its domain.

富比尼定理（英语：Fubini’s theorem）是数学分析中有关重积分的一个定理，由数学家圭多·富比尼在1907年提出。富比尼定理给出了使用逐次积分的方法计算双重积分的条件。在这些条件下，不仅能够用逐次积分计算双重积分，而且交换逐次积分的顺序时，积分结果不变。Tonelli定理由数学家 Leonida Tonelli在1909年提出，与富比尼定理相似，但是是应用于非负函数而不是可积函数。

https://en.wikipedia.org/wiki/Fubini%27s_theorem