a new proof for the banach-zarecki theorem: a light on integrability and continuity
نویسندگان
چکیده
to demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the banach-zareckitheorem is presented on the basis of the radon-nikodym theoremwhich emphasizes on measure-type properties of the lebesgueintegral. the banach-zarecki theorem says that a real-valuedfunction $f$ is absolutely continuous on a finite closed intervalif and only if it is continuous and of bounded variation when itsatisfies lusin's condition. in the present proof indeed a moregeneral result is obtained for the jordan decomposition of $f$.
منابع مشابه
A new proof for the Banach-Zarecki theorem: A light on integrability and continuity
To demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the Banach-Zareckitheorem is presented on the basis of the Radon-Nikodym theoremwhich emphasizes on measure-type properties of the Lebesgueintegral. The Banach-Zarecki theorem says that a real-valuedfunction $F$ is absolutely continuous on a finite closed intervalif and only if it is continuo...
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to demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the banach-zareckitheorem is presented on the basis of the radon-nikodym theoremwhich emphasizes on measure-type properties of the lebesgueintegral. the banach-zarecki theorem says that a real-valuedfunction $f$ is absolutely continuous on a finite closed intervalif and only if it is continuo...
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عنوان ژورنال:
bulletin of the iranian mathematical societyناشر: iranian mathematical society (ims)
ISSN 1017-060X
دوره 39
شماره 5 2013
کلمات کلیدی
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