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Grigore Ciurea:On the Henstock and McShane integrability, p.285-294

Abstract:

It is known that any Lebesgue integrable function is McShane integrable, and in fact we know only McShane's proof. In the first part of this paper we provide another proof of this result, and in the second part, we shall study the Lebesgue measurability of the Henstock integrable functions.We shall show that any function which is Henstock integrable is Lebesgue measurable, and thus we shall prove in a different way from the former proof from Y.Kubota, the Lebesgue measurability of the McShane integrable functions. We also present six corollaries of the others two results, some of them being already known.

Key Words: Henstock integral, Lebesgue integral, McShane integral.

2000 Mathematics Subject Classification: Primary: 26A24,
Secondary: 26A39, 26A42, 28A20.

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