On Functions with Summable Approximate Peano Derivative
نویسندگان
چکیده
منابع مشابه
Essential Supremum and Supremum of Summable Functions
Let D lR N , 0 < (D) < +1 and f : D ! lR is an arbitrary summable function. Then the function F() := R fx2D:f(x)g (f(x) ?) dd (2 lR) is continuous, non-negative, non-increasing, convex, and has almost everywhere the derivative F 0 () = ?f ]. Further on, it holds ess supf = supf 2 lR : F() > 0g, where ess supf denotes the essential supremum of f. These properties can be used for computing esssup...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1976
ISSN: 0002-9939
DOI: 10.2307/2040861