Abstract
It is shown that the notion of the length of an interval defines a measure on the ring generated by left-closed-right-open intervals in the real line ℝ. Using the method of Carathéodory, the Lebesgue measure is constructed on ℝ and its important properties are studied. Generalizations to ℝN,N ≥ 2, are also described. The property of translation invariance, and its consequences, are discussed.
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© 2019 Hindustan Book Agency 2019 and Springer Nature Singapore Pte Ltd.
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Kesavan, S. (2019). The Lebesgue measure. In: Measure and Integration. Texts and Readings in Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-13-6678-9_2
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DOI: https://doi.org/10.1007/978-981-13-6678-9_2
Publisher Name: Springer, Singapore
Online ISBN: 978-981-13-6678-9
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