Packing Measures and Dimensions on Cartesian Products
نویسندگان
چکیده
Packing measures Pg(E) and Hewitt-Stromberg measures νg(E) and their relatives are investigated. It is shown, for instance, that for any metric spaces X, Y and any Hausdorff functions f , g ν(X) ·P(Y ) 6 P(X × Y ). The inequality for the corresponding dimensions is established and used for a solution of a problem of Hu and Taylor: If X ⊆ Rn, then inf{dimPX × Y − dimPY : Y ⊆ R} = lim inf Xn↗X dimBXn. Corresponding dimension inequalities for products of measures are established. 2010 Mathematics Subject Classification: 28A78, 28A80, 54E35.
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