© 2015, Springer-Verlag Berlin Heidelberg. In this paper it is shown that if μ is a finite Radon measure in Rd which is n-rectifiable and 1≤p≤2, then (Formula Presented),where (Formula Presented),with the infimum taken over all the n-planes L⊂Rd. The (Formula Presented) coefficients are the same as the ones considered by David and Semmes in the setting of the so called uniform n-rectifiability. An analogous necessary condition for n-rectifiability in terms of other coefficients involving some variant of the Wasserstein distance W1 is also proved.
|Journal||Calculus of Variations and Partial Differential Equations|
|Publication status||Published - 1 Dec 2015|