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Absolutely Continuous Functions of Rado, Reichelderfer, and Malý

✍ Scribed by Marianna Csörnyei

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
274 KB
Volume
252
Category
Article
ISSN
0022-247X

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✦ Synopsis

Let C ‫ޒ‬ denote the set of all continuous functions f : ‫ޒ‬ ª ‫ޒ‬ with 0 Ž n . n compact support. For a function f g C ‫ޒ‬ and measurable set A ; ‫ޒ‬ 0 Ž . let f, A denote the oscillation of f on A. We denote the Lebesgue Ž . n measure of A by A . Let K ; ‫ޒ‬ be a fixed symmetric convex set of 0 non-empty interior, and let K K denote the set of all ''balls'' of ‫ޒ‬ n in the norm defined by K . In other words, we put 0 K K s c q dK : c g ‫ޒ‬ n , d g ‫ޒ‬ .

Ä 4 0 where the supremum is taken over every sequence of disjoint sets K , K , . . . g K K. We say that f satisfies the K K-Rado᎐Reichelderfer condi-1 2 tion, or f is K K-RR, if there exists an absolutely continuous finite measure on ‫ޒ‬ n , for which

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