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math.MG2018
The Entropy of Cantor--like measures
Kathryn E. Hare, Kevin G. Hare, Brian P. M. Morris +1
By a Cantor-like measure we mean the unique self-similar probability measure satisfying where $% S_{i}(x)=\frac{x}{d}+\frac{i}{d}\cdo…
math.MG2018
Quasi-doubling of self-similar measures with overlaps
Kathryn Hare, Kevin Hare, Sascha Troscheit
The Assouad and quasi-Assouad dimensions of a metric space provide information about the extreme local geometric nature of the set. The Assouad dimension of a set has a measure the…