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A Sard type theorem for Borel mappings. (English) Zbl 0834.28002
The author proves a Sard type theorem for Borel mappings \(f : \mathbb{R}^m \to \mathbb{R}^n\), where \(n \leq m\). If for the \(n\)-dimensional Hausdorff measure \(H^n\) of every Borel subset \(A \subset \mathbb{R}^m\) \[ H^n (f(A)) \leq C \cdot H^n (A) \] for some constant \(C\) then \(\dim_H (f^{-1} (y)) \leq m - n\) for almost all \(y\) in \(\mathbb{R}^n\).

MSC:
28A75 Length, area, volume, other geometric measure theory
28A78 Hausdorff and packing measures
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