Interchanging iterated integration
Author: Lawrence Lessner
Journal: Proc. Amer. Math. Soc. 68 (1978), 295-299
MSC: Primary 28A35
MathSciNet review: 0473134
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Abstract: If is a measurable, real valued, finite a.e. function on , then necessary and sufficient conditions are given for the two iterated Lebesgue integrals of to be equal and finite by employing Saks' theorem on the convergence of a sequence of finite measures and the Vitali convergence theorem. The conditions, more general than those of either Fubini's or Tonelli's theorems in this case, are applied to an example of a nonintegrable function to show that its iterated integrals are in fact equal and finite.
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Keywords: Iterated integrals, Saks' theorem, Fubini-Tonelli's theorem, Vitali convergence theorem
Article copyright: © Copyright 1978 American Mathematical Society