A NEW PROOF FOR THE BANACH-ZARECKI THEOREM: A LIGHT ON INTEGRABILITY AND CONTINUITY

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MAHDIPOUR SHIRAYEH A.; ESHRAGHI H.

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ISSN: 2588-4824

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Paper Information

Journal: BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY Year:2013 | Volume:39 | Issue:5 Page(s): 805-819

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Title

A NEW PROOF FOR THE BANACH-ZARECKI THEOREM: A LIGHT ON INTEGRABILITY AND CONTINUITY

Author(s)

MAHDIPOUR SHIRAYEH A. | ESHRAGHI H. | Issue Writer Certificate

Keywords

BANACH-ZARECKI THEOREM

RADON-NIKODYM THEOREM

LUSIN’S CONDITION

Abstract

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. In the present proof indeed a more general result is obtained for the Jordan decomposition of F.

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APA: Copy

MAHDIPOUR SHIRAYEH, A., & ESHRAGHI, H.. (2013). A NEW PROOF FOR THE BANACH-ZARECKI THEOREM: A LIGHT ON INTEGRABILITY AND CONTINUITY. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 39(5), 805-819. SID. https://sid.ir/paper/613571/en

Vancouver: Copy

MAHDIPOUR SHIRAYEH A., ESHRAGHI H.. A NEW PROOF FOR THE BANACH-ZARECKI THEOREM: A LIGHT ON INTEGRABILITY AND CONTINUITY. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY[Internet]. 2013;39(5):805-819. Available from: https://sid.ir/paper/613571/en

IEEE: Copy

A. MAHDIPOUR SHIRAYEH, and H. ESHRAGHI, “A NEW PROOF FOR THE BANACH-ZARECKI THEOREM: A LIGHT ON INTEGRABILITY AND CONTINUITY,” BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol. 39, no. 5, pp. 805–819, 2013, [Online]. Available: https://sid.ir/paper/613571/en

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