The centered hausdorff measure of the Sierpiński gasket
We show that the centered Hausdorff measure, Cs(S), with s=log3log2, of the Sierpiński gasket S, is C-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 Cs(S) is A-computable (alg...
| Autores: | , , |
|---|---|
| Formato: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/94973 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/94973 |
| Access Level: | acceso abierto |
| Palavra-chave: | 5 Sierpiński Gasket Hausdorff Measures Density of Measures Computability of Fractal Measures Ciencias Matemáticas (Matemáticas) Análisis matemático Geometría Análisis numérico 12 Matemáticas 1204 Geometría 1202 Análisis y Análisis Funcional |
| Resumo: | We show that the centered Hausdorff measure, Cs(S), with s=log3log2, of the Sierpiński gasket S, is C-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 Cs(S) is A-computable (algorithmic-computable) in the sense that there is an algorithm that converges to Cs(S), with explicit error bounds. Using this algorithm we show that Cs(S)∼1.0049. |
|---|