Abstract
It will be convenient to extend the domain of an integral to include certain ℝ* valued functions, and to extend the integral to an ℝ* valued functional on the larger domain. We make this extension and subsequently phrase the Beppo Levi theorem and Fatou’s lemma in this context. A more serious use of the new construct is then made in the study of product integrals and product measures.
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© 1988 Springer-Verlag New York Inc.
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Kelley, J.L., Srinivasan, T.P. (1988). Integrals* and Products. In: Measure and Integral. Graduate Texts in Mathematics, vol 116. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4570-4_8
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DOI: https://doi.org/10.1007/978-1-4612-4570-4_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8928-9
Online ISBN: 978-1-4612-4570-4
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