## 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

### Keywords:

box dimension; residual subset; typical measure; Baire category
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