Abstract
The theory developed in this chapter deals with Lebesgue measure for the sake of simplicity. However, all we need (except for the section where we discuss the Riemann integration) is the property of m being a measure, i.e. a countably additive (extended-) real-valued function µ defined on a σ-field F of subsets of a fixed set Ω. Therefore, the theory developed for the measure space (ℝ, M, m) in the following sections can be extended virtually without change to an abstractly given measure space (Ω, F, µ).
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© 2004 Springer-Verlag London Limited
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Capiński, M., Kopp, P.E. (2004). Integral. In: Measure, Integral and Probability. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-4471-0645-6_4
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DOI: https://doi.org/10.1007/978-1-4471-0645-6_4
Publisher Name: Springer, London
Print ISBN: 978-1-85233-781-0
Online ISBN: 978-1-4471-0645-6
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