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After the correction of an inaccurate result in the reference, the authoruses five different methods, and gets five different inequalities on theHausdorff measure of the Cartesian product of the middle third Cantor set withitself: $$H^s (C\times C)\leq 1.548563$$ $$H^s (C\times C)\leq 1.504975$$ $$H^s(C\times C)\leq 1.502878$$ $$H^s (C\times C)\leq 1.503263$$ $$H^s (C\timesC)\leq 1.502483.$$ The main theory of this paper is the best among them, whichis $$H^s (C\times C)\leq 1.502483.$$

A Better Upper Bound of Hausdorff Measure of the Cartesian Product of the Middle Third Cantor Set with Itself Compare to Others'