Do self-similar sets with positive Lebesgue measure contain an interval?

✍ Scribed by Keqiang Dong; Pengjian Shang

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 354 KB
• Volume: 23
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/j.aml.2009.09.013

✦ Synopsis

a b s t r a c t

This paper is concerned with the question whether each self-similar set on R 1 with positive Lebesgue measure contains an interval. We show that it is true for two instances: One is the self-similar set with respect to two similitudes; the other is the uniformly discrete selfsimilar set with respect to finite similitudes.