Decompose a set into sets of Hausdorff-dimension n-1 - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-18T08:52:35Z http://mathoverflow.net/feeds/question/75331 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/75331/decompose-a-set-into-sets-of-hausdorff-dimension-n-1 Decompose a set into sets of Hausdorff-dimension n-1 Christian 2011-09-13T16:40:14Z 2011-09-13T17:24:55Z <p>Assume we can decompose a set $A$ in $\mathbb{R^n}$ of Hausdorff-dimension n into sets $(A_t)$ $t\in [0,1]$ of Hausdorff-dimension n-1 whose n-1-dimensional volume is known (for example is zero). </p> <p>Are there any possibilities beside the coarea-formula that allow us to say something about the measure of A?</p>