Abstract
This chapter has two functions: Throughout the book it has served as an Appendix, to which the reader was referred for definitions, arguments, and results about measures and integrals. It will now serve as a functional analyst’s dream of the ideal short course in measure theory. Thus, we shall develop the theory of Radon integrals ( = Radon measures, cf. 6.3.4) on a locally compact Hausdorff space, assuming full knowledge of topology and topological vector spaces. This theory takes as point of departure an integral (a positive linear functional) on the minimal class of topologically relevant functions on X, namely, the class C c (X) of continuous functions with compact supports. The integral is extended by monotonicity to a larger class of (integrable) functions and the measure appears, post festum, as the value of the integral on characteristic functions.
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© 1989 Springer Science+Business Media New York
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Pedersen, G.K. (1989). Integration Theory. In: Analysis Now. Graduate Texts in Mathematics, vol 118. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1007-8_6
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DOI: https://doi.org/10.1007/978-1-4612-1007-8_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6981-6
Online ISBN: 978-1-4612-1007-8
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