On the measure of products from the middle-third Cantor set

2021/04/20 by Luca Marchese, Marchese, Luca
Mathematics · #Approximation Theory and Sequence Spaces #Dynamical Systems (math.DS) #FOS: Mathematics #Metric Geometry (math.MG) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2104.09939

openalex publication_date 2021/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove upper and lower bounds for the Lebesgue measure of the set of products xy with x and y in the middle-third Cantor set. Our method is inspired by Athreya, Reznick and Tyson, but a different subdivision of the Cantor set provides a more rapidly converging approximation formula.

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