Topological Riesz spaces and measure theory
نویسندگان
چکیده
منابع مشابه
COPIES OF c0 AND `∞ IN TOPOLOGICAL RIESZ SPACES
The paper is concerned with order-topological characterizations of topological Riesz spaces, in particular spaces of measurable functions, not containing Riesz isomorphic or linearly homeomorphic copies of c0 or `∞.
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There is a rich literature on the study of Bessel and Riesz potentials on the Euclidean space R, see for example the books [23, 20, 1, 16] and the references therein. However, little is known on how to extend the Bessel and Riesz potentials to metric measure spaces in a reasonable way. This issue is interesting in that it is closely related with the study of various current topics, such as the ...
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Let X be a topological space and μ be a nonatomic finite measure on a σ-algebra Σ containing the Borel σ-algebra of X. We say μ is weakly outer regular, if for every A ∈ Σ and ǫ > 0, there exists an open set O such that μ(A\O) = 0 and μ(O\A) < ǫ. The main result of this paper is to show that if f, g ∈ L1(X,Σ, μ) with R
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The integral in noncommutative geometry (NCG) involves a non-standard trace called a Dixmier trace. The geometric origins of this integral are well known. From a measure-theoretic view, however, the formulation contains several difficulties. We review results concerning the technical features of the integral in NCG and some outstanding problems in this area. The review is aimed for the general ...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1976
ISSN: 0001-8708
DOI: 10.1016/0001-8708(76)90206-1