AN INTERMEDIATE VALUE PROPERTY OF FRACTAL DIMENSIONS OF CARTESIAN PRODUCT
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Given two metric spaces [Formula: see text], it is well known that, [Formula: see text] where [Formula: see text], [Formula: see text] denote, respectively, the Hausdorff and packing dimension of [Formula: see text]. In this paper, we show that, for any [Formula: see text], there exist [Formula: see text] such that the following equalities hold simultaneously: [Formula: see text] This complete the related results of Wei et al. [C. Wei, S. Y. Wen and Z. X. Wen, Remarks on dimensions of Cartesian product sets, Fractals 24(3) (2016) 1650031].
1996 ◽
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