期刊论文

Liu, C.

中文

数学学报：中文版

0583-1431

2012

55

6

1013-1018

华中师范大学中央高校基本科研业务费项目（CCNU11A01028）；

本校为第一且通讯机构

设L_(a,b)是由实数列{a_n}诱导的Rademacher级数的水平集,其级数部分和的上极限为b,下极限为a.本文利用自然数密度和符号空间上的局部Holder连续性,证明了当数列{a_n}通项趋于零且不属于l~1时,水平集L_(a,b)的Hausdorff维数为1.

Let La,b be the level set of Redemacher series, being induced by a real sequence (an), for which the upper limit of the part summation is b and the lower limit isa. By the tools named the density of natural numbers and local Holder continuity in the symbol space, the author proved that the Hausdorff dimension of La,b is one if the sequence (an)n=1∞ doesn't be...