MATHEMATICA BOHEMICA, Vol. 129, No. 2, pp. 141-157 (2004)

McShane equi-integrability and
Vitali's convergence theorem

Jaroslav Kurzweil, Stefan Schwabik

Jaroslav Kurzweil, Stefan Schwabik, Matematicky ustav AV CR, Zitna 25, 115 67 Praha 1, Czech Republic, e-mail:, schwabik@math.

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. \endgraf 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 (MSC2000): 26A39

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