| Title:
|
Abstract Riemann integrability and measurability (English) |
| Author:
|
de Amo, E. |
| Author:
|
del Campo, R. |
| Author:
|
Carrillo, M. Díaz |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
4 |
| Year:
|
2009 |
| Pages:
|
1123-1139 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that the spectral sets of any positive abstract Riemann integrable function are measurable but (at most) a countable amount of them. In addition, the integral of such a function can be computed as an improper classical Riemann integral of the measures of its spectral sets under some weak continuity conditions which in fact characterize the integral representation. (English) |
| Keyword:
|
finitely additive integration |
| Keyword:
|
localized convergence |
| Keyword:
|
integral representation |
| Keyword:
|
weak continuity conditions |
| Keyword:
|
horizontal integration |
| MSC:
|
26A42 |
| MSC:
|
28C05 |
| idZBL:
|
Zbl 1224.28030 |
| idMR:
|
MR2563583 |
| . |
| Date available:
|
2010-07-20T16:08:48Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140542 |
| . |
| Reference:
|
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