Open Access
2004-2005 Tangential behavior of functions and conical densities of Hausdorff measures.
Ville Suomala
Author Affiliations +
Real Anal. Exchange 30(2): 843-854 (2004-2005).


We construct a $C^1$-function $f\colon [0,1]\to \mathbb{R}$ such that for almost all $x\in(0,1)$, there is $r>0$ for which $f(y)>f(x)+f'(x)(y-x)$ when $y\in(x,x+r)$ and $f(y)< f(x)+f'(x)(y-x)$ when $y\in(x-r,x)$. The existence of such functions is related to a problem concerning conical density properties of Hausdorff measures on $\mathbb{R}^n$. We also discuss the tangential behavior of typical $C^1$-functions, using an improvement of Jarník's theorem on essential derived numbers


Download Citation

Ville Suomala. "Tangential behavior of functions and conical densities of Hausdorff measures.." Real Anal. Exchange 30 (2) 843 - 854, 2004-2005.


Published: 2004-2005
First available in Project Euclid: 15 October 2005

zbMATH: 1146.26305
MathSciNet: MR2177441

Primary: 26A24
Secondary: 28A78

Keywords: Conical density , essential derived number.

Rights: Copyright © 2004 Michigan State University Press

Vol.30 • No. 2 • 2004-2005
Back to Top