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The Federer theorem deals with the “massiveness” of the set of critical values for a t t -smooth map acting from R m \mathbb R^m to R n \mathbb R^n : it claims that the Hausdorff p p -measure of this set is zero for certain p p . If n ≥ m n\ge m , it has long been known that the assumption of that theorem relating the parameters m , n , t , p m,n,t,p is sharp. Here it is shown by an example that this assumption is also sharp for n > m n>m .

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