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Published October 1966 | public
Journal Article

Some examples of normed Köthe spaces


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.

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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