关于Hausdorff测度与Lebesgue测度的若干相关性质
[内容摘要]： 本文利用大学本科所学的测度论知识推导了维Hausdorff测度的若干与Lebesgue测度类似和相关的性质，讨论了所涉及的Vitali-覆盖引理、Caratheodory引理等工具的推广情形，以及在整数维情形下Hausdorff测度与Lebesgue测度的等价性。在本文最后举例对Hausdorff测度与Lebesgue测度进行了比较和分析。
[关键词] Hausdorff测度、Lebesgue测度、外测度、Borel集、正则测度、域、Vitali-覆盖
Abstract With the help of the measure theory learned in university, the author deduced several properties of dimensioned Hausdorff measure, which are similar and pertinent to Lebesgue measure in the thesis. The author also demonstrated the corollaries of the tools of Vitali-covering lemma and Caratheodory lemma,and the equivalent between Hausdorff measure and Lebesgue measure in integer dimensioned circumstances. Finally, the author compared and analyzed the two measure together by exemplifying.
Key words Hausdorff measure Lebesgue measure outer measure Borel set regular measure field Vitali-covering.
