In this paper we investigate some connections between Hausdorff measures, Hölder functions and analytic sets in terms of images of zero-derivative sets and level sets. We characterize in terms of Hausdorff measures and descriptive complexity subsets which are
(1) the image under some function of the set of points where the derivatives of first orders are zero
(2) the set of points where the level sets of some function are perfect
(3) the set of points where the level sets of some function are uncountable.
Cite this article
Emma D'Aniello, Level Sets of Hölder Functions and Hausdorff Measures. Z. Anal. Anwend. 21 (2002), no. 3, pp. 691–707DOI 10.4171/ZAA/1103