| Title:
|
Order boundedness and weak compactness of the set of quasi-measure extensions of a quasi-measure (English) |
| Author:
|
Lipecki, Zbigniew |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
56 |
| Issue:
|
3 |
| Year:
|
2015 |
| Pages:
|
331-345 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\mathfrak M$ and $\mathfrak R$ be algebras of subsets of a set $\Omega $ with $\mathfrak M\subset\mathfrak R$, and denote by $E(\mu )$ the set of all quasi-measure extensions of a given quasi-measure $\mu $ on $\mathfrak M$ to $\mathfrak R$. We give some criteria for order boundedness of $E(\mu )$ in $ba(\mathfrak R)$, in the general case as well as for atomic $\mu $. Order boundedness implies weak compactness of $E (\mu )$. We show that the converse implication holds under some assumptions on $\mathfrak M$, $\mathfrak R$ and $\mu $ or $\mu $ alone, but not in general. (English) |
| Keyword:
|
linear lattice |
| Keyword:
|
order bounded |
| Keyword:
|
additive set function |
| Keyword:
|
quasi-measure |
| Keyword:
|
atomic |
| Keyword:
|
extension |
| Keyword:
|
convex set |
| Keyword:
|
extreme point |
| Keyword:
|
weakly compact |
| MSC:
|
06F20 |
| MSC:
|
28A12 |
| MSC:
|
28A33 |
| MSC:
|
46A55 |
| MSC:
|
46B42 |
| idZBL:
|
Zbl 06486997 |
| idMR:
|
MR3390280 |
| DOI:
|
10.14712/1213-7243.2015.130 |
| . |
| Date available:
|
2015-07-09T20:49:08Z |
| Last updated:
|
2017-10-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144348 |
| . |
| Reference:
|
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