Some authors give generalizations of Tonelli's theorem to some measure spaces that are not σ-finite but these generalizations often add conditions that immediately reduce the problem to the σ-finite case. For example, one could take the σ-algebra on "A"×"B" to be that generated by the product of subsets of finite measure, rather than that generated by all products of measurable subsets, though this has the undesirable consequence that the projections from the product to its factors "A" and "B" are not measurable. Another way is to add the condition that the support of "f" is contained in a countable union of products of sets of finite measure. gives some rather technical extensions of Tonelli's theorem to some non σ-finite spaces. None of these generalizations have found any significant applications outside abstract measure theory, largely because almost all measure spaces of practical interest are σ-finite.