title: Measure Theory: A First Course
author:  Carlos S Kubrusly 
description: "As a book for a first course, the author has definitely come up with a well-balanced interesting text: not too threatening for beginners and interesting enough for someone with some knowledge of the subject."<b> --Professor N. Levan, UCLA (USA)</b>
zlib_text: Donald L. CohnBirkhäuser Advanced Texts Basler LehrbücherMeasure Theory2nd ed.
  2013Second Edition10.1007/978-1-4614-6956-8_1© Springer Science+Business Media
  New York 2013
  
  # 1\. Measures
  
  Donald L. Cohn1
  
  (1)
  
  Department of Mathematics and Computer Science, Suffolk University, Boston,
  MA, USA
  
  Abstract
  
  In the most common construction of the Lebesgue integral of a function, the
  definition of the integral assumes that one knows the sizes of subsets of the
  function's domain. In Chapter 1 we introduce measures, the basic tool for
  dealing with such sizes. The first two sections of the chapter are abstract
  (but elementary). Section 1.1 looks at sigma-algebras, the collections of sets
  whose sizes we measure, while Section 1.2 introduces measures themselves. The
  heart of the chapter is in the following two sections, where we look at some
  general techniques for constructing measures (Section 1.3) and at the basic
  properties of Lebesgue measure (Section 1.4). The chapter ends with Sections
  1.5