Abstract
We need further information on the structure of integrable functions if our theory of integration is to be conveniently usable. For example, if J on M is the Daniell extension of the pre-integral induced by a length function, must every continuous function with compact support belong to M? The answer is not self-evident, although it had certainly better be “yes”! We shall presently find criteria for integrability involving a set theoretic (measurability) requirement, and a magnitude requirement.
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© 1988 Springer-Verlag New York Inc.
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Kelley, J.L., Srinivasan, T.P. (1988). Measurability and σ-Simplicity. In: Measure and Integral. Graduate Texts in Mathematics, vol 116. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4570-4_6
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DOI: https://doi.org/10.1007/978-1-4612-4570-4_6
Publisher Name: Springer, New York, NY
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