By means of the idea of [2]（Jia Baoguo,J.Math.Anal.Appl.In press） and the self.similarity of Sierpinski carpet, we obtain the lower and upper bounds of the Hausdorff Measure of Sierpinski carpet, which can approach ...By means of the idea of [2]（Jia Baoguo,J.Math.Anal.Appl.In press） and the self.similarity of Sierpinski carpet, we obtain the lower and upper bounds of the Hausdorff Measure of Sierpinski carpet, which can approach the Hausdorff Measure of Sierpinski carpet infinitely.展开更多
In this paper, we construct a self-similar set which has a best covering but it is not the natural covering, thus negate the conjecture on self-similar sets posed by Z. Zhou in 2004.
文摘By means of the idea of [2]（Jia Baoguo,J.Math.Anal.Appl.In press） and the self.similarity of Sierpinski carpet, we obtain the lower and upper bounds of the Hausdorff Measure of Sierpinski carpet, which can approach the Hausdorff Measure of Sierpinski carpet infinitely.
基金Supported in part by the Foundations of the National Natural Science Committee(No.10572154)Jiangxi Province Natural Science Committee(No.0611005)the Foundation of Education Ministry, Jiangxi Province(No.[2006]239), China
文摘In this paper, we construct a self-similar set which has a best covering but it is not the natural covering, thus negate the conjecture on self-similar sets posed by Z. Zhou in 2004.
