Some examples of normed Köthe spaces
Some examples of normed Köthe spaces
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赋范柯德空间的一些例子
DOI：
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发表时间：
1966
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通讯作者：
A. Zaanen
中科院分区：
文献类型：
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作者：
W. Luxemburg;A. Zaanen
设X是一个非空点集，μ是X中的可数可加非负测度.我们假设Caratheodory扩张过程已经应用于μ，所以μ被定义在其上的σ-域Λ不能被Caratheodory扩张过程的另一个应用所扩大。此外，将假设μ是（完全）（σ-有限的，即，X是有限个或可数个有限测度集的并集。因此，三元组（X，Λ，μ）在通常的术语中是（完全）σ-有限测度空间。符号d μ将表示整个集合X上的积分（关于μ），并且χ E = χ E（x）将代表集合E <$X的特征函数。
Let X be a non-empty point set, and μ a countably additive and non-negative measure in X. We assume that the Caratheodory 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 Caratheodory 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.