| Title:
|
Order convergence of vector measures on topological spaces (English) |
| Author:
|
Khurana, Surjit Singh |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
133 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
19-27 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be a completely regular Hausdorff space, $E$ a boundedly complete vector lattice, $C_{b}(X)$ the space of all, bounded, real-valued continuous functions on $X$, $\mathcal{F}$ the algebra generated by the zero-sets of $X$, and $\mu \: C_{b}(X) \rightarrow E$ a positive linear map. First we give a new proof that $\mu $ extends to a unique, finitely additive measure $ \mu \: \mathcal{F} \rightarrow E^{+}$ such that $\nu $ is inner regular by zero-sets and outer regular by cozero sets. Then some order-convergence theorems about nets of $E^{+}$-valued finitely additive measures on $\mathcal{F}$ are proved, which extend some known results. Also, under certain conditions, the well-known Alexandrov’s theorem about the convergent sequences of $\sigma $-additive measures is extended to the case of order convergence. (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:
|
28B05 |
| MSC:
|
28B15 |
| MSC:
|
28C05 |
| MSC:
|
28C15 |
| MSC:
|
46B42 |
| MSC:
|
46G10 |
| MSC:
|
47B65 |
| idZBL:
|
Zbl 1199.28008 |
| idMR:
|
MR2400148 |
| DOI:
|
10.21136/MB.2008.133944 |
| . |
| Date available:
|
2009-09-24T22:34:00Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133944 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| . |
