Abstract
Let X be an arbitrary set. A collection A of subsets of X is an algebra on X if
-
(a)
X ∈ A,
-
(b)
for each set A that belongs to A the set A c belongs to A,
-
(c)
for each finite sequence A 1,..., A n of sets that belong to A the set \( \cup _{i = 1}^n {\rm A}_i \) belongs to A, and
-
(d)
for each finite sequence A 1,..., A n of sets that belong to A the set \( \cap _{i = 1}^n {\rm A}_i \) belongs to A.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Notes
Halmos [38] is a standard reference for the theory of measure and integration. The books by Bartle [1], Berberian [2], Hewitt and Stromberg [42], Munroe [64], Royden [73], Rudin [75], Segal and Kunze [78], and Wheeden and Zygmund [87] are also well-known and useful. Books by Billingsley [3] and Jacobs [47] have just appeared. The reader should see Billingsley [3] for applications to probability theory, Rudin [75] for a great variety of applications to analysis, and Wheeden and Zygmund [87] for applications to harmonic analysis. Jacobs [47] contains an enormous amount of material. Federer [32], lonescu Tulcea and Ionescu Tulcea [46], and Rogers [71] treat topics in measure theory that are not touched upon here.
Theorem 1.6.1 is due to Dynkin [31] (see also Blumenthal and Getoor [9]).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1980 Springer Science+Business Media New York
About this chapter
Cite this chapter
Cohn, D.L. (1980). Measures. In: Measure Theory. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-0399-0_1
Download citation
DOI: https://doi.org/10.1007/978-1-4899-0399-0_1
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4899-0401-0
Online ISBN: 978-1-4899-0399-0
eBook Packages: Springer Book Archive