The Denjoy-Clarkson property with respect to Hausdorff measures for the gradient mapping of functions of several variables
Annales de l'Institut Fourier, Volume 58 (2008) no. 2, pp. 405-428.

We construct a differentiable function f:R n R (n2) such that the set (f) -1 (B(0,1)) is a nonempty set of Hausdorff dimension 1. This answers a question posed by Z. Buczolich.

On construit une fonction différentiable f:R n R (n2) telle que l’ensemble (f) -1 (B(0,1)) est non vide et sa dimension de Hausdorff est 1. C’est une réponse à une question posée par Z. Buczolich.

DOI: 10.5802/aif.2356
Classification: 26B05, 28A75
Keywords: Denjoy–Clarkson property, gradient, Hausdorff measure, infinite game
Mot clés : propriété de Denjoy-Clarkson, gradient, mesure de Hausdorff, jeu infini

Zelený, Miroslav 1

1 Charles University Faculty of Mathematics and Physics Sokolovská 83 186 75 Praha 8 (Czech Republic)
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Zelený, Miroslav. The Denjoy-Clarkson property with respect to Hausdorff measures for the gradient mapping of functions of several variables. Annales de l'Institut Fourier, Volume 58 (2008) no. 2, pp. 405-428. doi : 10.5802/aif.2356. https://aif.centre-mersenne.org/articles/10.5802/aif.2356/

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