AN INTERMEDIATE VALUE PROPERTY OF FRACTAL DIMENSIONS OF CARTESIAN PRODUCT.

Given two metric spaces , it is well known that, where , denote, respectively, the Hausdorff and packing dimension of . In this paper, we show that, for any , there exist such that the following equalities hold simultaneously: 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]. [ABSTRACT FROM AUTHOR]