Fubini's theorem has some rather technical extensions to the case when "X" and "Y" are not assumed to be σ-finite . The main extra complication in this case is that there may be more than one product measure on "X"×"Y". Fubini's theorem continues to hold for the maximal product measure, but can fail for other product measures. For example, there is a product measure and a non-negative measurable function "f" for which the double integral of |"f"| is zero but the two iterated integrals have different values; see the section on counterexamples below for an example of this. Tonelli's theorem and the Fubini–Tonelli theorem (stated below) can fail on non σ-finite spaces even for the maximal product measure.