10.1007/978-3-642-85997-7_22
doi
https://doi.org/10.1007/978-3-642-85997-7_22
337-350
1966
Some Examples of Normed Köthe Spaces
2022-01-01T19:07
en
procedure
applications
Carathéodory extension procedure
non-negative measure
set
chapters
extension procedure
1966-01-01
Carathéodory procedure
measures
non-empty point set
chapter
Let X be a non-empty point set, and μ a countably additive and non-negative measure in X. We assume that the Carathéodory extension procedure has already been applied to μ, so that the σ-field Λ on which μ is defined cannot be enlarged by another application of the Carathéodory procedure. Furthermore, it will be assumed that μ is (totally) (σ-finite, i.e., X is the union of a finite or countable number of sets of finite measure. Hence, the triple (X, Λ, μ) is a (totally) σ-finite measure space in the usual terminology. The notation ∫ d μ will denote integration (with respect to μ) over the whole set X, and χE = χE(x) will stand for the characteristic function of the set E ⊂ X.
field λ
false
point sets
https://scigraph.springernature.com/explorer/license/
pub.1021280102
dimensions_id
W. A. J.
Luxemburg
Pasadena, USA
Leiden, Niederlande
Pasadena, USA
Leiden, Niederlande
978-3-642-85999-1
978-3-642-85997-7
Contributions to Functional Analysis
A. C.
Zaanen
Mathematical Sciences
Pure Mathematics
Springer Nature - SN SciGraph project
Springer Nature