Some Examples of Normed Köthe Spaces

W. A. J. Luxemburg and A. C. Zaanen

A chapter in Contributions to Functional Analysis, 1966, pp 337-350 from Springer

Abstract: 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.

Date: 1966
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DOI: 10.1007/978-3-642-85997-7_22

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