Wednesday, June 13, 2012

1206.2602 (Ali Mahdipour-Shirayeh et al.)

A new proof for the Banach-Zarecki theorem: A light on integrability and

Ali Mahdipour-Shirayeh, Homayoon Eshraghi
To demonstrate more visibly the close relation between the continuity and integrability, a new proof for the Banach-Zarecki theorem is presented on the basis of the Radon-Nikodym theorem which emphasizes on measure-type properties of the Lebesgue integral. The Banach-Zarecki theorem says that a real-valued function F is absolutely continuous on a finite closed interval if and only if it is continuous and of bounded variation when it satisfies Lusin's condition (N).
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