2008/07/23 by Pablo Shmerkin, Shmerkin, Pablo
Computer Science · Mathematics · #28A80 #37C45 #Advanced Topology and Set Theory #Cellular Automata and Applications #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.CA #math.DS #msc:28A80 #msc:37C45
paper · pdf · doi:10.48550/arxiv.0807.3709
15 pages. Expository notes, will not be submitted
arxiv created 2008/07/23 · openalex publication_date 2008/07/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.