Cn Functions, Hausdorff Measures, and Analytic Sets

✍ Scribed by Emma D'Aniello; Udayan B. Darji

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 211 KB
• Volume: 164
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1006/aima.2001.2012

✦ Synopsis

We characterize in terms of Hausdorff measures and descriptive complexity subsets M ı R which are

(1) the image under some C n function f of the set of points where derivatives of first n orders are zero, (2) the set of points where the level sets of some C n function are perfect, and

(3) the set of points where the level sets of some C n function are uncountable.