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MATHEMATICA BOHEMICA, Vol. 129, No. 2, pp. 141-157 (2004)
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#
McShane equi-integrability and

Vitali's convergence theorem

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Jaroslav Kurzweil, Stefan Schwabik

* 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. \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

**Full text of the article:**

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