Some Examples of Normed Köthe Spaces View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1966

AUTHORS

W. A. J. Luxemburg , A. C. Zaanen

ABSTRACT

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. More... »

PAGES

337-350

Book

TITLE

Contributions to Functional Analysis

ISBN

978-3-642-85999-1
978-3-642-85997-7

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-642-85997-7_22

DOI

http://dx.doi.org/10.1007/978-3-642-85997-7_22

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1021280102


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