摘要
In this paper,we consider sets of points with some restricts on the digits of theirα-Lroth expansions.More precisely,for any countable partitionα={An,n∈N}of the unit interval I,we completely determine the Hausdorf dimensions of the sets F(α,φ)=x=[l1(x),l2(x),...]α∈I:ln(x)φ(n),n 1,whereφis an arbitrary positive function defined on N satisfyingφ(n)→∞as n→∞.
In this paper,we consider sets of points with some restricts on the digits of theirα-Lroth expansions.More precisely,for any countable partitionα={An,n∈N}of the unit interval I,we completely determine the Hausdorf dimensions of the sets F（α,φ）=x=[l1（x）,l2（x）,...]α∈I：ln（x）φ（n）,n 1,whereφis an arbitrary positive function defined on N satisfyingφ（n）→∞as n→∞.
基金
supported by National Natural Science Foundation of China (Grant No.11071090)
关键词
HAUSDORFF维数
点集
可数
函数
Hausdorff dimension, the a-Ltiroth expansion, expanding, expansive exponent, eventually de-creasing
