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Pointwise Dimensions and Rényi Dimensions

Ryszard Rudnicki
Proceedings of the American Mathematical Society
Vol. 130, No. 7 (Jul., 2002), pp. 1981-1982
Stable URL: http://www.jstor.org/stable/2699800
Page Count: 2
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Abstract

We prove that the local lower and upper pointwise dimensions of a probability measure μ are bounded from below by the lower generalized dimension $\underline{D}_\mu (q)$ for q > 1 and from above by the upper generalized dimension $\underline{D}_\mu (q)$ for q < 1.

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