A Straight Line On The Fractal Set Of Hausdorff Measure

In this paper,it's considered that how to position and calculate the Hausdorff measure of some fractals on the line.We give the definition of extended Cantor structure and draw a conclusion that the Hausdorff measure of dimension s of the fractal (extended Cantor set ),which is decided by the extended Cantor structure, just is sth power of the diameter of the fractal,where the s is the Hausdorff dimension of the fractal .It is showed that if the contraction system composed of some monotonous contractions on the line, the convex closure of the fractal decided by it can be decided by the fixed point or the image of fixed point under these contractions.