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An elementary proof of the theorem that absolute gauge integrability implies Lebesgue integrability
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 3, pp. 621-633.

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It is commonly known that absolute gauge integrability, or Henstock-Kurzweil (H-K) integrability implies Lebesgue integrability. In this article, we are going to present another proof of that fact which utilizes the basic definitions and properties of the Lebesgue and H-K integrals.
Classification : 26A39, 26A42
Keywords: absolute integrability; gauge Integral; H-K integral; Lebesgue integral 
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Myers, Timothy. An elementary proof of the theorem that absolute gauge integrability implies Lebesgue integrability. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 3, pp. 621-633. http://geodesic.mathdoc.fr/item/CMJ_2010__60_3_a2/