The Entropy of Cantor--like measures
By a Cantor-like measure we mean the unique self-similar probability measure $μ$ satisfying $μ=\sum_{i=0}^{m-1}p_{i}μ\circ S_{i}^{-1}$ where $% S_{i}(x)=\frac{x}{d}+\frac{i}{d}\cdot \frac{d-1}{m-1}$ for integers $2\leq d 0$, $\sum p_{i}=1$. In the uniform case ($p_{i}=1/m$ for all $i$) we show how one can compute the entropy and Hausdorff dimension to arbitrary precision. In the non-uniform case we find bounds on the entropy.
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