Hausdorff Centered Measures Of Non-uniform 3-part Cantor Set

In this dissertation we study the Hausdorff centered measure of the non-uniform 3-part Cantor set.That is the set generated by linear iterated function system consisting of three maps with different contraction ratios.We give the definition of the Hausdorff centered measure. First we establish a relation between Hausdorff centered measure and the upper density of corresponding self-similar set.we define a probability measure,and estimateμof some special intervals,and construct a subset F(β,λ,3)of the attractor K(β,λ,3)In certain condition, we proveμ(F(β,λ,3))=1.From these relation,in certain condition,we get the upper bound and the lower bound of the non-uniform 3-part Cantor set.This dissertation consists of three sections.In the first one,we will briefly talk about the history and background of fractal geometry,the main tools used in fractal geometry.In the second one,we main introduce Preliminaries and main results of the article.In third two,we will give the main results of this dissertation.