一个与Hausdorff测度相关的秩零定理

A Rank Zero Theorem Concerned to Hausdorff Measures

利用 Morse广义临界点引理和 L ebesgue密度定理以及 Vitali覆盖引理 ,证明一个与 Hausdorff测度相关的秩零定理 .将要解决的转化为一些公式的精细估计 ,并由这个秩零定理推出 ,当 r =0时 Arthur Sard在196

The aim of this work is to prove a rank zero theorem concerned to Hausdorff measures. The main method is to use the generalized Morse criticality lemma, Lebesgue density theorem and Vitali covering lemma to transfer this problem to the accute estimate of some formulas, hence to deduce and to prove an open statement posed by Arthur Sard in 1965 while r=0.