## Some generic properties of concentration dimension of measure.(English)Zbl 1177.28014

Summary: Let $$K$$ be a compact quasi self-similar set in a complete metric space $$X$$ and let $$\mathfrak{M}_{1} (K)$$ denote the space of all probability measures on $$K$$, endowed with the Fortet–Mourier metric. We will show that for a typical (in the sense of Baire category) measure in $$\mathfrak{M}_{1} (K)$$ the lower concentration dimension is equal to the Hausdorff dimension of $$K$$.

### MSC:

 28A78 Hausdorff and packing measures 54E45 Compact (locally compact) metric spaces 37B99 Topological dynamics
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