A Sard type theorem for Borel mappings

doi:https://doi.org/10.4064/cm-67-2-217-221

Open AccessArticle10.4064/cm-67-2-217-221

A Sard type theorem for Borel mappings

Piotr Hajłasz-1994-01-01-Colloquium Mathematicum

TL;DRAbstract

We find a condition for a Borel mapping f : R m R n which implies that the Hausdorff dimension of f -1 (y) is less than or equal to m -n for almost all y R n .

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We find a condition for a Borel mapping f : R m R n which implies that the Hausdorff dimension of f -1 (y) is less than or equal to m -n for almost all y R n .

Keywords

MathematicsType (biology)Hausdorff dimensionDimension (graph theory)Borel setHausdorff spaceDiscrete mathematicsPure mathematics

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