Order of integration (source code)

= Order of integration

The sequence in which variables are integrated in an <iterated integral>. Reversing the order changes the slicing of the <domain of integration>, often requiring more than one integral. <Fubini's theorem> permits interchange for absolutely integrable functions, while <Tonelli's theorem> permits nonnegative measurable integrands even when the integral is infinite. Conditional convergence requires additional care; geometric reversal alone is not a general justification for interchanging improper integrals.