Fubini's theorem

Conditions for switching order of integration in calculus

Fubini's theorem gives the conditions under which a double integral can be computed as an iterated integral, i.e. by integrating in one variable at a time. Intuitively, just as the volume of a loaf of bread is the same whether one sums over standard slices or over long thin slices, the value of a double integral does not depend on the order of integration when the hypotheses of the theorem are satisfied.

From Wikipedia, under CC BY-SA. More on occurri.