Cardinal Functions of Purely Atomic Measures
نویسندگان
چکیده
منابع مشابه
Purely Non-atomic Weak L P Spaces
Let (Ω,Σ, μ) be a purely non-atomic measure space, and let 1 < p < ∞. If L(Ω,Σ, μ) is isomorphic, as a Banach space, to L(Ω,Σ, μ) for some purely atomic measure space (Ω,Σ, μ), then there is a measurable partition Ω = Ω1 ∪Ω2 such that (Ω1,Σ ∩ Ω1, μ|Σ∩Ω1) is countably generated and σ-finite, and that μ(σ) = 0 or ∞ for every measurable σ ⊆ Ω2. In particular, L(Ω,Σ, μ) is isomorphic to l.
متن کاملInformation Measures via Copula Functions
In applications of differential geometry to problems of parametric inference, the notion of divergence is often used to measure the separation between two parametric densities. Among them, in this paper, we will verify measures such as Kullback-Leibler information, J-divergence, Hellinger distance, -Divergence, … and so on. Properties and results related to distance between probability d...
متن کاملLocal cardinal functions of H-closed spaces
The cardinal functions of pseudocharacter, closed pseudocharacter, and character are used to examine H-closed spaces and to contrast the differences between Hclosed and minimal Hausdorff spaces. An H-closed space X is produced with the properties that |X| > 22 ψ(X) and ψ(X) > 2ψ(X).
متن کاملA Banach Space Characterization of Purely Atomic Measure Spaces
It is well known [4, p. 265; 3] that the space 7,i[0, l] is not isomorphic with a conjugate space. At the other extreme, it is also well known that h is isometric with the conjugate space of Co. Each of these is an example of a space of all real-valued integrable functions over a measure space (T, p), a major difference between them being that the measure space underlying 7_i[0, l] has no atoms...
متن کاملSimilarity Metrics: A Formal Unification of Cardinal and Non-Cardinal Similarity Measures
In [9] we introduced a formal framework for constructing ordinal similarity measures, and suggested how this might also be applied to cardinal measures. In this paper we will place this approach in a more general framework, called similarity metrics. In this framework, ordinal similarity metrics (where comparison returns a boolean value) can be combined with cardinal metrics (returning a numeri...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Results in Mathematics
سال: 2020
ISSN: 1422-6383,1420-9012
DOI: 10.1007/s00025-020-01260-x