Hausdorff measure and level sets of typical continuous mappings in Euclidean spaces

Kirchheim, Bernd

doi:10.1090/S0002-9947-1995-1260171-7

Hausdorff measure and level sets of typical continuous mappings in Euclidean spaces
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by Bernd Kirchheim

Trans. Amer. Math. Soc. 347 (1995), 1763-1777

DOI: https://doi.org/10.1090/S0002-9947-1995-1260171-7

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Abstract:

We determine the Hausdorff dimension of level sets and of sets of points of multiplicity for mappings in a residual subset of the space of all continuous mappings from ${\mathbb {R}^n}$ to ${\mathbb {R}^m}$.

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