1. Abstract Riemann integrability and measurability
- Creator:
- de Amo, E., del Campo, R., and M. Díaz
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- finitely additive integration, localized convergence, integral representation, weak continuity conditions, and horizontal integration
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public