Families of plane curves having translates in a set of measure zero
作者:
Eric Sawyer,
期刊:
Mathematika
(WILEY Available online 1987)
卷期:
Volume 34,
issue 1
页码: 69-76
ISSN:0025-5793
年代: 1987
DOI:10.1112/S0025579300013292
出版商: London Mathematical Society
数据来源: WILEY
摘要:
AbstractWe construct a universal function φ on the real line such that, for every continuously differentiable functionfthe range off– φ has measure zero. We then apply this to obtain results on curve packing that generalize the Besicovitch set. In particular, we show that given a continuously differentiable family of measurable curves, there exists a plane set of measure zero containing a translate of each curve in the family. Examples are given to show that the differentiability hypothesis cannot be weakened to a Lipschitz condition of order α for any 0<α<1.
点击下载:
PDF
(448KB)
返 回