Upper Bound Estimates Of Hausdorff Measures Of The Sierpinski Carpet And The Sierpinski Cube Sponge

This article is divided into four parts: The first part concerns history of fractal geometry, some construction and research methods of fractal sets. The second part gives the Hausdorff measure and dimension of fractals; The third part is to estimate upper bounds for the Hausdorff measure of the Sierpinski carpet H~s ( E)≤1.38497468782; The fourth part obtains a upper bound for the Hausdorff measure of Sierpinski cube sponge H~s( E )≤3.05587422.