一类非齐次Moran集的Hausdorff测度

金艳玲; 魏毅强

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一类非齐次Moran集的Hausdorff测度

更新时间：2026-09-14

- 一类非齐次Moran集的Hausdorff测度
- 一类非齐次Moran集的Hausdorff测度
- Issue 1, (2011)
- 作者机构：
  
  1. 山西大学商务学院,山西,太原,030031
  2. 太原理工大学理学院
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2011
- 稿件说明：
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金艳玲, 魏毅强. 一类非齐次Moran集的Hausdorff测度[J]. 2011, (1).
DOI：

金艳玲, 魏毅强. 一类非齐次Moran集的Hausdorff测度[J]. 2011, (1). DOI：

摘要

利用质量分布原理与自然覆盖

对一类满足强分离条件的非齐次Moran集的Hausdorff测度进行了研究.证明了主要结论:对于由({nk}k≥1

{Φk}k≥1

{mk}k≥1)确定的非齐次Moran集E

它的s维Hausdorff测度是各同级相似比ci

j的s次幂的和

随i从1到k作乘积

并求当压缩次数k趋于无穷大时的乘积的极限值.

Abstract

With the mass distribution theory and natural cover

the paper studied a kind of Hausedorff measure of non-homogeneous Moran sets which satisfy the strong separation condition

and proved the following conclusions: for the non-homogeneous Moran sets E determined by({nk}k≥1

{Φk}k≥1

{mk}k≥1)

its s dimension Hausedorff measure is got by multiplying the sum of s powers of the same level ratio ci

j from 1 to k according to i.The limit is also derived on the condition that k

the times of compression

tends to ∞.

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