Abstract
In this chapter we shall consider the relationship between a real Borel measure v and the Lebesgue measure m. Key to such relationships is Theorem 4.24, which shows that for each non-negative integrable real function f, the set function
defines a (Borel) measure v on (ℝ, M). The natural question to ask is the converse: exactly which real Borel measures can be found in this way? We shall find a complete answer to this question in this chapter, and in keeping with our approach in Chapters 5 and 6, we shall phrase our results in terms of general measures on an abstract set Ω.
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© 2004 Springer-Verlag London Limited
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Capiński, M., Kopp, P.E. (2004). The Radon—Nikodym theorem. In: Measure, Integral and Probability. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-4471-0645-6_7
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DOI: https://doi.org/10.1007/978-1-4471-0645-6_7
Publisher Name: Springer, London
Print ISBN: 978-1-85233-781-0
Online ISBN: 978-1-4471-0645-6
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