McShane equi-integrability and Vitali’s convergence theorem.(English)Zbl 1051.26012

Summary: The McShane integral of functions $$f\: I \to \mathbb R$$ 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.

MSC:

 26B99 Functions of several variables 26A39 Denjoy and Perron integrals, other special integrals
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