设La,b是由实数列{an}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{an}通项趋于零且不属于l1时, 水平集La,b的Hausdorff维数为1.
Abstract
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 is a. 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 belong to l1 with the general term tending to zero.
关键词
Rademacher级数 /
上密度 /
Hausdorff维数 /
水平集
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Key words
Rademacher series /
upper density /
Hausdorff dimension /
the level set
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参考文献
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脚注
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基金
华中师范大学中央高校基本科研业务费项目(CCNU11A01028)
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