05-130 F, Germinet, S. Tcheremchantsev

Generalized fractal dimensions on the negative axis for non compactly supported measures (265K, PDF) Apr 8, 05

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Abstract. We study the finiteness of the generalized fractal dimensions $D^\pm_\mu(q)$ (also called Hentschel-Procaccia dimensions) for a non compactly supported measure $\mu$ on a complete metric space, and for $q<0$. The upper dimensions are shown to be always infinite. We then provide a sufficient condition for the lower dimensions to bemeasures infinite. Optimality of our theorems is proved by constructing explicit measures on $\mathbb{R}$.

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