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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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