Average Best m-term Approximation

We introduce the concept of average best m-term approximation widths with respect to a probability measure on the unit ball or the unit sphere of $ell_{p}^{n}$ . We estimate these quantities for the embedding $id:ell_{p}^{n}toell_{q}^{n}$ with 0<p??q??? for the normalized cone and surface measure. Furthermore, we consider certain tensor product weights and show that a typical vector with respect to such a measure exhibits a strong compressible (i.e., nearly sparse) structure. This measure may therefore be used as a random model for sparse signals.