JournalszaaVol. 21, No. 3pp. 691–707

Level Sets of Hölder Functions and Hausdorff Measures

  • Emma D'Aniello

    Università degli Studi di Napoli, Caserta, Italy
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Abstract

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 MRM \subseteq \mathbb R which are
(1) the image under some Cm,αC^{m, \alpha} function ff of the set of points where the derivatives of first nn orders are zero
(2) the set of points where the level sets of some Cm,αC^{m, \alpha} function are perfect
(3) the set of points where the level sets of some Cm,αC^{m, \alpha} 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. 691–707

DOI 10.4171/ZAA/1103