Packing measures and dimensions on cartesian products
Packing measures Pg(E) and Hewitt-Stromberg measures vg(E) and their relatives are investigated. It is shown, for instance, that for any metric spaces X, Y and any Hausdorff functions f, g vg (X) • Ph (Y) ≤ Pgh (X x Y). The inequality for the corresponding dimensions is established and used for a so...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:107337 |
| Acceso en línea: | https://ddd.uab.cat/record/107337 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_57213_06 |
| Access Level: | acceso abierto |
| Palabra clave: | Packing measure Lower packing measure Packing dimension Lower Cartesian product |
| Sumario: | Packing measures Pg(E) and Hewitt-Stromberg measures vg(E) and their relatives are investigated. It is shown, for instance, that for any metric spaces X, Y and any Hausdorff functions f, g vg (X) • Ph (Y) ≤ Pgh (X x Y). The inequality for the corresponding dimensions is established and used for a solution of a problem of Hu and Taylor: If X ⊆ Rn, then inf {dimpX x Y - dimpY : Y ⊆ Rn } = lim inf dimB Xn. Corresponding dimension inequalities for products of measures are established. |
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