Skip to main content
eScholarship
Open Access Publications from the University of California

UC Irvine

UC Irvine Electronic Theses and Dissertations bannerUC Irvine

Arithmetic Sums of Nearly Affine Cantor Sets

Abstract

For a compact set K ⊂ R1 and a family {Cλ}λ∈J of dynamically defined Cantor sets sufficiently close to affine with dimH K +dimH Cλ > 1 for all λ ∈ J, we prove that the sum K+Cλ has positive Lebesgue measure for almost all values of the parameter λ. As a corollary, we show that generically the sum of two affine Cantor sets has positive Lebesgue measure provided the sum of their Hausdorff dimensions is greater than one.

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View