1. Convergence theorems for the Birkhoff integral
- Creator:
- Balcerzak, Marek and Potyrała, Monika
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Birkhoff integral, convergence theorems, and vector valued functions
- Language:
- English
- Description:
- We give sufficient conditions for the interchange of the operations of limit and the Birkhoff integral for a sequence $(f_n)$ of functions from a measure space to a Banach space. In one result the equi-integrability of $f_n$'s is involved and we assume $f_n\to f$ almost everywhere. The other result resembles the Lebesgue dominated convergence theorem where the almost uniform convergence of $(f_n)$ to $f$ is assumed.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public