摘要
研究了Koch曲线的Hausdorff测度的上、下界的估计,得到两个结论.其一,考虑了一种部分覆盖,利用这个覆盖计算出了Koch曲线的Hausdorff测度的一个新的上界估计值Hs(K)≤14099566×38476s≈0.587847293.其二,导出一个估计式μ(V)≤1.88|V|s,并结合质量分布原理得到了Koch曲线的Hausdorff测度的一个更好的下界估计值Hs(K)≥0.531914893.
In this paper,the lower bound and upper estimation of the Hausdorff measure about the Koch curve is investigated.Some new conclusions are obtained as follows.The first,some part-coverage was considered.Using this coverage,a new upper bound estimation value of the Koch curve Hs（K）≤40961956×（87634）s≈0.587847293 is obtained.On the other hand,we derived the inequality μ（V）≤1.88｜V｜s.Using this inequality and the mass distribution principle,a better lower bound estimation value of the Koch curve Hs（K）≥0.531914893 is obtained.
出处
《南阳师范学院学报》
CAS
2010年第12期25-27,共3页
Journal of Nanyang Normal University
