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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-1-4612-4570-4_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8928-9
Online ISBN: 978-1-4612-4570-4
eBook Packages: Springer Book Archive