Typical Lq-Dimensions of Measures

• Autores: Lars Olsen
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 146, Nº 2, 2005, págs. 143-157
• Idioma: inglés
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• Resumen

  • For a probability measure µ on a subset of , the lower and upper Lq-dimensions of order are defined by We study the typical behaviour (in the sense of Baire¿s category) of the Lq-dimensions and . We prove that a typical measure µ is as irregular as possible: for all q = 1, the lower Lq-dimension attains the smallest possible value and the upper Lq-dimension attains the largest possible value.