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Some examples of normed Köthe spaces

Luxemburg, W. A. J. and Zaanen, A. C. (1966) Some examples of normed Köthe spaces. Mathematische Annalen, 162 (3). pp. 337-350. ISSN 0025-5831. https://resolver.caltech.edu/CaltechAUTHORS:20181003-155854579

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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 χ E = χ E (x) will stand for the characteristic function of the set E ⊂ X.


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https://doi.org/10.1007/bf01369107DOIArticle
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Additional Information:© Springer-Verlag 1966. (Received July 1, 1965) Dedicated to ProfessorG. Köthe on the occasion of his sixtieth birthday on December 25, 1965. The preparation of this paper was supported in part by the National Science Foundation of the U.S.A. under grant NSF-G 213 and in part by the Netherlands Organization for the Advancement of Pure Research (Z.W.O.).
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Funding AgencyGrant Number
NSFG 213
Nederlandse Organisatie voor Zuiver-Wetenschappelijk Onderzoek (ZWO)UNSPECIFIED
Issue or Number:3
Record Number:CaltechAUTHORS:20181003-155854579
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20181003-155854579
Official Citation:Luxemburg, W.A.J. & Zaanen, A.C. Math. Ann. (1966) 162: 337. https://doi.org/10.1007/BF01369107
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90114
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:06 Oct 2018 22:26
Last Modified:03 Oct 2019 20:22

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