Geodesic
McShane equi-integrability and Vitali’s convergence theorem
Mathematica Bohemica, Tome 129 (2004) no. 2, pp. 141-157

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MR Zbl
The McShane integral of functions $f\:I\rightarrow \mathbb{R}$ 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.
The McShane integral of functions $f\:I\rightarrow \mathbb{R}$ 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.
DOI : 10.21136/MB.2004.133903
Classification : 26A39, 26B99
Keywords: McShane integral; Vitali convergence theorem; equi-integrability 
Kurzweil, Jaroslav; Schwabik, Štefan. McShane equi-integrability and Vitali’s convergence theorem. Mathematica Bohemica, Tome 129 (2004) no. 2, pp. 141-157. doi: 10.21136/MB.2004.133903
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