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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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