Rings of sets

Hari Bercovici, Arlen Brown and Carl Pearcy
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Hari Bercovici: Indiana University, Department of Mathematics
Arlen Brown: Indiana University, Department of Mathematics
Carl Pearcy: Texas A&M University, Department of Mathematics

Chapter Chapter 1 in Measure and Integration, 2016, pp 1-18 from Springer

Abstract: Abstract It is a familiar fact of elementary calculus that the integral of a function exists only if the function is continuous, or nearly so. In the theory of the Lebesgue integral integral Lebesgue Lebesgue integral, with which we are concerned in this book, continuity is replaced by a significantly less stringent requirement known as measurability measurability. This concept, in turn, is defined in terms of a certain type of collection of sets, called a σ $$ \sigma $$ -algebra σ $$ \sigma $$ -algebra, and so we begin with a brief look at this and some related concepts.

Keywords: Ordinal Number; Countable Union; Symmetric Difference; Finite Union; Countable Intersection (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-29046-1_1

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