THE CENTERED HAUSDORFF MEASURE OF THE SIERPIŃSKI GASKET

Author:

LLORENTE MARTA1ORCID,MERA MARÍA EUGENIA2ORCID,MORÁN MANUEL23ORCID

Affiliation:

1. Departamento de Análisis Económico: Economía Cuantitativa, Universidad Autónoma de Madrid, Campus de Cantoblanco, 28049 Madrid, Spain

2. Departamento de Análisis Económico y Economía Cuantitativa, Universidad Complutense de Madrid, Campus de Somosaguas, 28223 Madrid, Spain

3. Institute of Interdisciplinary Mathematics (IMI), Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid, Spain

Abstract

We show that the centered Hausdorff measure, [Formula: see text] with [Formula: see text] of the Sierpiński gasket [Formula: see text], is [Formula: see text]-computable (continuous-computable), in the sense that its value is the solution of the minimization problem of a continuous function on a compact domain. We also show that [Formula: see text] is [Formula: see text]-computable (algorithmic-computable) in the sense that there is an algorithm that converges to [Formula: see text] with explicit error bounds. Using this algorithm we show that [Formula: see text].

Funder

Universidad Complutense de Madrid and the Banco de Santander

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Geometry and Topology,Modeling and Simulation

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Irregularity Index and Spherical Densities of the Penta-Sierpinski Gasket;Mediterranean Journal of Mathematics;2023-10-27

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