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Measure Theory

Chapter
Part of the Universitext book series (UTX)

Abstract

The reader has undoubtedly already encountered the notion of measure, though perhaps under a different name. For instance, the area of a plane figure, the length of a rectifiable curve, the volume, the mass, are all examples of measures. The chapter covers the following material: algebras and sigma-algebras of sets; Borel sets; finite and countable additivity of measures; atoms, atomic and non-atomic measures; extension of measures; the Lebesgue measure on the interval and on the real line; Lebesgue’s theorem on the differentiability of monotone functions.

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and Computer ScienceV. N. Karazin Kharkiv National UniversityKharkivUkraine

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