Restrictions of continuous functions

被引：6
|
作者：
Kahane, Jean-Pierre [1 ]
Katznelson, Yitzhak [2 ]
机构：
[1] Univ Paris 11, Math Lab, F-91405 Orsay, France
[2] Stanford Univ, Dept Math, Stanford, CA 94305 USA
来源：
ISRAEL JOURNAL OF MATHEMATICS | 2009年 / 174卷 / 01期
关键词：
Disjoint Interval; Monotone Sequence; Gaussian Stationary Process; Lipschitz Class; Minkowski Dimension;
D O I：
10.1007/s11856-009-0114-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Given a continuous (or just measurable) real-valued function on [0, 1] and a closed subset E aS, [0, 1], denote by f| (E) the restriction of f to E. f| (E) can be "better behaved" than f and we discuss the existence, for every f, or every f in some class, of sets E that are substantial in terms of fractal dimension, such that f| (E) has bounded total variation, or is monotone, or satisfies a given modulus of continuity.
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页码：269 / 284
页数：16
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