Morse-Sard theorem for d.c. curves

2006/12/18 by D. Pavlica, Pavlica, D.
Mathematics · #26A51 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:26A51

paper · pdf · doi:10.48550/arxiv.math/0612505

4 pages

arxiv created 2006/12/19 · arxiv updated 2009/12/01

Abstract

Let f:I→ X be a d.c. mapping, where I⊂ \R is an open interval and X a Banach space. Let C_f be the set of critical points of f. We prove that f(C_f) has zero 1/2-dimensional Hausdorff measure.

Related

• On some universal Morse-Sard type Theorem
• Morse--Sard theorem and Luzin N-property: a new synthesis result for Sobolev spaces
• Sard properties for polynomial maps in infinite dimension
• The Dubovitski\uı-Sard Theorem in Sobolev Spaces
• Hausdorff measure of critical set for Luzin N condition