Integrals and measures

Hari Bercovici, Arlen Brown and Carl Pearcy
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Hari Bercovici: Indiana University, Department of Mathematics
Arlen Brown: Indiana University, Department of Mathematics
Carl Pearcy: Texas A&M University, Department of Mathematics

Chapter Chapter 3 in Measure and Integration, 2016, pp 43-73 from Springer

Abstract: Abstract In the language of modern integration theory the term integral integral refers to a number of somewhat different concepts, arrived at through a variety of constructions and definitions. About the only thing that can be said about integration in reasonable generality is that an integral on a space X is a linear transformation linear transformation transformation -linear that is defined on a vector space vector space -of functions of functions on X and satisfies certain continuity continuity requirements. As regards the Lebesgue integral -Lebesgue integral, Lebesgue integral however, matters are in a much less chaotic state. Indeed, while a considerable number of different definitions and L: a Lebesgue integral constructions ℒ $$\mathcal{L}$$ : the domain of a Lebesgue integral can be found in the literature, there is unanimous agreement on what a Lebesgue integral is. We provide an axiomatic characterization.

Keywords: Lebesgue Integral; Modern Integration Theory; Axiomatic Characterization; Extended Real Number; Lebesgue-Borel Measure (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-29046-1_3

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DOI: 10.1007/978-3-319-29046-1_3

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