Strict inequality in the box-counting dimension product formulas

2010/07/23 by Nick Sharples, Sharples, Nick · 3 citations
Mathematics · #28A75 #Advanced Topology and Set Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Point processes and geometric inequalities #math.MG #msc:28A75

paper · pdf · doi:10.48550/arxiv.1007.4222

arxiv created 2010/07/23 · openalex publication_date 2010/07/23 · arxiv updated 2010/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is known that the upper box-counting dimension of a Cartesian product satisfies the inequality dim_B(F× G)≤ dim_B(F) + dim_B(G) whilst the lower box-counting dimension satisfies the inequality dim_LB(F× G)≥ dim_LB(F) + dim_LB(G). We construct Cantor-like sets to demonstrate that both of these inequalities can be strict.

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