Classifying Cantor Sets by their Fractal Dimensions

2009/05/12 by Carlos Cabrelli, Cabrelli, Carlos A., Kathryn E. Hare +3 · 1 citation
Mathematics · #28A78 #28A80 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · doi:10.48550/arxiv.0905.1980

openalex publication_date 2009/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we study Cantor sets defined by monotone sequences, in the sense of Besicovitch and Taylor. We classify these Cantor sets in terms of their h-Hausdorff and h-Packing measures, for the family of dimension functions h, and characterize this classification in terms of the underlying sequences.

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