THE ZYGMUND MORSE-SARD THEOREM

被引：22

作者：

NORTON, A ^{[1
]}

机构：

[1] UNIV TEXAS,DEPT MATH,AUSTIN,TX 78712

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 1994年 / 4卷 / 03期

关键词：

DIFFERENTIABILITY; LIPSCHITZ; MEASURE ZERO; MODULUS OF CONTINUITY; MORSE-SARD; ZYGMUND;

D O I：

10.1007/BF02921589

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The classical Morse-Sard Theorem says that the set of critical values of f : R(n+k) --> R(n) has Lebesgue measure zero if f is-an-element-of C(k+1). We show the C(k+1) smoothness requirement can be weakened to C(k+Zygmund). This is corollary to the following theorem: For integers n > m > r > 0, let s = (n - r)/(m - r); if f : R(n) --> R(m) belongs to the Lipschitz class LAMBDA(s) and E is a set of rank r for f, then f(E) has measure zero.

引用

页码：403 / 424

页数：22