 Then formula_97 converges absolutely, converges conditionally or diverges according to the corresponding behavior of formula_98

The situation is different for the Lebesgue integral, which does not handle bounded and unbounded domains of integration separately ("see below").The fact that the integral of formula_84 is unbounded in the examples above implies that formula_79 is also not integrable in the Lebesgue sense.In fact, in the Lebesgue theory of integration, given that formula_79 is measurable, formula_79 is (Lebesgue) integrable if and only if formula_84 is (Lebesgue) integrable.