1. McShane equi-integrability and Vitali’s convergence theorem
- Creator:
- Kurzweil, Jaroslav and Schwabik, Štefan
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- McShane integral, Vitali convergence theorem, and equi-integrability
- Language:
- English
- Description:
- The McShane integral of functions f : I → ! defined on an m-dimensional interval I is considered in the paper. This integral is known to be equivalent to the Lebesgue integral for which the Vitali convergence theorem holds. For McShane integrable sequences of functions a convergence theorem based on the concept of equi-integrability is proved and it is shown that this theorem is equivalent to the Vitali convergence theorem.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public