Random intersections of thick Cantor sets

Author:
Roger L. Kraft

Journal:
Trans. Amer. Math. Soc. **352** (2000), 1315-1328

MSC (1991):
Primary 28A80; Secondary 58F99

DOI:
https://doi.org/10.1090/S0002-9947-99-02464-2

Published electronically:
September 20, 1999

MathSciNet review:
1653359

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Abstract: Let , be Cantor sets embedded in the real line, and let , be their respective thicknesses. If , then it is well known that the difference set is a disjoint union of closed intervals. B. Williams showed that for some , it may be that is as small as a single point. However, the author previously showed that generically, the other extreme is true; contains a Cantor set for all in a generic subset of . This paper shows that small intersections of thick Cantor sets are also rare in the sense of Lebesgue measure; if , then contains a Cantor set for almost all in .

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Additional Information

**Roger L. Kraft**

Affiliation:
Department of Mathematics, Computer Science and Statistics, Purdue University Calumet, Hammond, Indiana 46323

Email:
roger@calumet.purdue.edu

DOI:
https://doi.org/10.1090/S0002-9947-99-02464-2

Keywords:
Cantor sets,
difference sets,
thickness

Received by editor(s):
October 14, 1997

Published electronically:
September 20, 1999

Additional Notes:
Research supported in part by a grant from the Purdue Research Foundation

Article copyright:
© Copyright 1999
American Mathematical Society