English

Moreira's Theorem on the arithmetic sum of dynamically defined Cantor sets

Dynamical Systems 2008-07-24 v1 Classical Analysis and ODEs

Abstract

We present a complete proof of a theorem of C.G. Moreira. Under mild checkable conditions, the theorem asserts that the Hausdorff dimension of the arithmetic sum of two dynamically defined Cantor subsets of the real line, equals either the sum of the dimensions or 1, whichever is smaller.

Keywords

Cite

@article{arxiv.0807.3709,
  title  = {Moreira's Theorem on the arithmetic sum of dynamically defined Cantor sets},
  author = {Pablo Shmerkin},
  journal= {arXiv preprint arXiv:0807.3709},
  year   = {2008}
}

Comments

15 pages. Expository notes, will not be submitted

R2 v1 2026-06-21T11:03:34.654Z