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

TL;DR

This paper provides a complete proof of Moreira's theorem, establishing that the Hausdorff dimension of the sum of two dynamically defined Cantor sets equals either their combined dimension or 1, under certain conditions.

Contribution

The paper offers a full proof of Moreira's theorem, clarifying conditions under which the dimension of the sum of Cantor sets is determined.

Findings

Hausdorff dimension of sum equals sum of dimensions or 1

Complete proof of Moreira's theorem provided

Conditions for dimension calculation clarified

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.