Title:
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Radon-Nikodym property (English) |
Author:
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Khurana, Surjit Singh |
Language:
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English |
Journal:
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Commentationes Mathematicae Universitatis Carolinae |
ISSN:
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0010-2628 (print) |
ISSN:
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1213-7243 (online) |
Volume:
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58 |
Issue:
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4 |
Year:
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2017 |
Pages:
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461-464 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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For a Banach space $E$ and a probability space $(X, \mathcal{A}, \lambda)$, a new proof is given that a measure $\mu: \mathcal{A} \to E$, with $\mu \ll \lambda$, has RN derivative with respect to $\lambda$ iff there is a compact or a weakly compact $C \subset E$ such that $|\mu |_{C} : \mathcal{A} \to [0, \infty]$ is a finite valued countably additive measure. Here we define $|\mu |_{C}(A) = \sup \{\sum_{k} |\langle \mu (A_{k}), f_{k}\rangle |\}$ where $\{A_{k}\}$ is a finite disjoint collection of elements from $\mathcal{A}$, each contained in $A$, and $\{f_{k}\}\subset E'$ satisfies $\sup_{k} |f_{k} (C)|\leq 1$. Then the result is extended to the case when $E$ is a Frechet space. (English) |
Keyword:
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liftings |
Keyword:
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lifting topology |
Keyword:
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weakly compact sets |
Keyword:
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Radon-Nikodym derivative |
MSC:
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28A51 |
MSC:
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28B05 |
MSC:
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28C05 |
MSC:
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46B22 |
MSC:
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46G05 |
MSC:
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46G10 |
MSC:
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60B05 |
idZBL:
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Zbl 06837079 |
idMR:
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MR3737118 |
DOI:
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10.14712/1213-7243.2015.228 |
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Date available:
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2017-12-12T06:46:38Z |
Last updated:
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2020-01-05 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/146990 |
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Reference:
|
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Reference:
|
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Reference:
|
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Reference:
|
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Reference:
|
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Reference:
|
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Reference:
|
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Reference:
|
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Reference:
|
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