Jaroslav Kurzweil, Stefan Schwabik, Matematicky ustav AV CR, Zitna 25, 115 67 Praha 1, Czech Republic, e-mail: kurzweil@math.cas.cz, schwabik@math.cas.cz
Abstract: The McShane integral of functions $f I\to\Bbb R$ 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.
Keywords: McShane integral
Classification (MSC 2000): 26A39
Full text available as PDF (smallest), as compressed PostScript (.ps.gz) or as raw PostScript (.ps).
Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at myris@myris.cz.
