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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In this paper, we present a short proof of the following theorem due to Takeuchi. Theorem A. (Takeuchi [Ta], [Su]) Let Ω be a pseudoconvex domain with C 2-smooth boundary in a Kähler manifold M 2n and r = d(x, bΩ). Suppose that the Kähler manifold M 2n has holomorphic bisectional curvature ≥ 1. Then the second fundamental form of bΩ (−t) satisfies: i∂ ¯ ∂(−r)(ζ, ¯ ζ) ≥ rζ 2 for all ζ ∈ T 1,0 x ...
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We present a new proof of Banaschewski's theorem stating that the completion lift of a uniform surjection is a surjection. The new procedure allows to extend the fact (and, similarly, the related theorem on closed uniform sublocales of complete uniform frames) to quasi-uniformities ("not necessarily symmetric uniformities"). Further, we show how a (regular) Cauchy point on a closed uniform subl...
متن کاملa 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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ژورنال
عنوان ژورنال: The Annals of Mathematical Statistics
سال: 1964
ISSN: 0003-4851
DOI: 10.1214/aoms/1177703581