Some Theorems Of Doubling Measure

Since 1895 Borel introduced his measure as a tool to measure sets,people have tried to construct various measures in different sets and spaces and is the core part of the fractal geometry. It is an object as well as one of the most important tool in the study fractal mathematics. We now list several important results of Hausdorff dimension with respect to the Lebesgue measure;In 1998 Wu proved that for every s> 0 and for every compact doubling metric space X,there is a doubling measure u on X and a subset E such that μ(E)= μ(X) and H8E)= 0; The proof of each of the above results is based on an appropriate doubling measure. In this paper, It contains three parts. In part one, we introduce the define of the doubling measure,In part two, we put the doubling measure to broaden the homogeneity measure up. In part three,we give the main conclusion of this paper.