%0 Journal Article
%T Hausdorff Measure for the Set of $m$-Adic Numbers without Neighboring Zeroes<br>限制零的m进制数集之Hausdorff测度
%A ZHONG Ting
%A ZHANG Qingqing
%A TANG Liang
%A <br>钟婷
%A 张菁菁
%A 汤亮
%J 系统科学与数学
%D 2008
%I 
%X For any integer $m\geq2$, let$F_m=\big\{x\in0,1): \{m^kx\}\geq \frac{1}{m^2},k\in N\big\}$,where $\{m^kx\}$ is the fractional part of $m^kx$. This paper gives the Hausdorff measure of $F_m$:\,$H^s(F_m)=(\frac{m^2-2}{m^2-1})^s$, where $s=\log_m\frac{m-1+\sqrt{(m-1)^2+4(m-1)}}{2}$ is the Hausdorff dimension of $F_m$.
%K m-adic
%K sequence of no double zeroes linked
%K mass distribution
%K Hausdorff dimension
%K Hausdorff measure<br>m进制数
%K 零不相邻序列
%K 质量分布
%K Hausdorff维数
%K Hausdorff测度
%K 进制
%K 数集
%K Hausdorff
%K 测度
%K NUMBERS
%K 维数
%K 整数表示
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=0CD45CC5E994895A7F41A783D4235EC2&aid=5DD962E1635F62E5C1825ECA84CAEB24&yid=67289AFF6305E306&vid=D3E34374A0D77D7F&iid=94C357A881DFC066&sid=A726E84831FE609B&eid=1918ADDC93A85779&journal_id=1000-0577&journal_name=系统科学与数学&referenced_num=0&reference_num=4