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On the box dimension of typical measures. (English) Zbl 1001.28002

Summary: Let \((X,\rho)\) be a complete metric space and let \(\mathcal M\) be the space of all probability Borel measures on \(X\). We give some estimations of the upper and lower box dimensions of the typical (in the sense of Baire category) measure in \(\mathcal M\).

MSC:

28A78 Hausdorff and packing measures
54E52 Baire category, Baire spaces
26A21 Classification of real functions; Baire classification of sets and functions
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