| Title:
|
Lattice-valued Borel measures. III. (English) |
| Author:
|
Khurana, Surjit Singh |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
44 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
307-316 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be a completely regular $T_{1}$ space, $E$ a boundedly complete vector lattice, $ C(X)$ $(C_{b}(X))$ the space of all (all, bounded), real-valued continuous functions on $X$. In order convergence, we consider $E$-valued, order-bounded, $\sigma $-additive, $\tau $-additive, and tight measures on X and prove some order-theoretic and topological properties of these measures. Also for an order-bounded, $E$-valued (for some special $E$) linear map on $C(X)$, a measure representation result is proved. In case $E_{n}^{*}$ separates the points of $E$, an Alexanderov’s type theorem is proved for a sequence of $\sigma $-additive measures. (English) |
| Keyword:
|
order convergence |
| Keyword:
|
tight and $\tau $-smooth lattice-valued vector measures |
| Keyword:
|
measure representation of positive linear operators |
| Keyword:
|
Alexandrov’s theorem |
| MSC:
|
28A33 |
| MSC:
|
28B15 |
| MSC:
|
28C05 |
| MSC:
|
28C15 |
| MSC:
|
46B42 |
| MSC:
|
46G10 |
| idZBL:
|
Zbl 1212.28009 |
| idMR:
|
MR2493427 |
| . |
| Date available:
|
2009-01-29T09:15:33Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119770 |
| . |
| Reference:
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