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Abstract Riemann integrability and measurability
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.
Creator
- de Amo, E.
- del Campo, R.
- M. Díaz
- Mariano Díaz
Subject
- finitely additive integration
- localized convergence
- integral representation
- weak continuity conditions
- horizontal integration
Type of item
- model:article
Creator
- de Amo, E.
- del Campo, R.
- M. Díaz
- Mariano Díaz
Subject
- finitely additive integration
- localized convergence
- integral representation
- weak continuity conditions
- horizontal integration
Type of item
- model:article
Providing institution
Aggregator
Rights statement for the media in this item (unless otherwise specified)
- http://creativecommons.org/licenses/by-nc-sa/4.0/
Rights
- policy:public
Place-Time
- 1123-1139
Source
- Czechoslovak Mathematical Journal | 2009 Volume:59 | Number:4
Identifier
- https://cdk.lib.cas.cz/client/handle/uuid:2a226ddb-2775-4317-8b05-2e8673baee6f
- uuid:2a226ddb-2775-4317-8b05-2e8673baee6f
- uuid:2a226ddb-2775-4317-8b05-2e8673baee6f
Format
- bez média
- svazek
Language
- eng
- eng
Providing country
- Czech Republic
Collection name
First time published on Europeana
- 2021-05-21T06:43:45.539Z
Last time updated from providing institution
- 2021-12-25T05:07:51.358Z