| Title:
|
Radon-Nikodym property (English) |
| Author:
|
Khurana, Surjit Singh |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
58 |
| Issue:
|
4 |
| Year:
|
2017 |
| Pages:
|
461-464 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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:
|
liftings |
| Keyword:
|
lifting topology |
| Keyword:
|
weakly compact sets |
| Keyword:
|
Radon-Nikodym derivative |
| MSC:
|
28A51 |
| MSC:
|
28B05 |
| MSC:
|
28C05 |
| MSC:
|
46B22 |
| MSC:
|
46G05 |
| MSC:
|
46G10 |
| MSC:
|
60B05 |
| idZBL:
|
Zbl 06837079 |
| idMR:
|
MR3737118 |
| DOI:
|
10.14712/1213-7243.2015.228 |
| . |
| Date available:
|
2017-12-12T06:46:38Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146990 |
| . |
| 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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| . |
