Hausdorff Measures and Hausdorff Dimensions of the Invariant Sets for Iterated Function Systems of Geometric Fractals

摘要

In this paper, we discuss Hausdorff measure and Hausdorff dimension. We also discuss iterated function systems (IFS) of the generalized Cantor sets and higher dimensional fractals such as the square fractal, the Menger sponge and the Sierpinski tetrahedron and show the Hausdorff measures and Hausdorff dimensions of the invariant sets for IFS of these fractals.