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, with which we are concerned in this book, continuity is replaced by a significantly less stringent requirement known as measurability. This concept, in turn, is defined in terms of a certain type of collection of sets, called a \( \sigma \) -algebra, and so we begin with a brief look at this and some related concepts.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Bercovici, H., Brown, A., Pearcy, C. (2016). Rings of sets. In: Measure and Integration. Springer, Cham. https://doi.org/10.1007/978-3-319-29046-1_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-29046-1_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-29044-7
Online ISBN: 978-3-319-29046-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)