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Pointwise dimensions and Rényi dimensions |
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| Authors: | Ryszard Rudnicki |
| Affiliation: | Institute of Mathematics, Polish Academy of Sciences and Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland |
| Abstract: | We prove that the local lower and upper pointwise dimensions of a probability measure  are bounded from below by the lower generalized dimension  for  and from above by the upper generalized dimension  for  . |
| Keywords: | Pointwise dimension generalized (R'enyi) dimension measure |
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