Two Types Of Fractal And Hausdorff Measure

In the first part of this article,the author introduces the defines of Hausdorff dimensoin and Hausdorff measure,and some relevant theories;In the second part of this article,using a plane-point representing system,the author construct the Siepinski carpets. And by this way,gets the Hausdorff measure of the Sierpinski carpets is a decreasing function as to the compressed ratio.Therefore,the author gets a range of the measure.In addition,the authors give a simple proof of a well-known result.In the third part of this article,using the theory of Marion and some methods,the author calculates the accurate Hausdorff measure of a fractal in the line.And generalizes this result to a general situation.