Certain representations of the Cuntz relations, and a question on   wavelets decompositions
  We compute the Coifman-Meyer-Wickerhauser measure $\mu$ for certain families of quadrature mirror filters (QMFs), and we establish that for a subclass of QMFs, $\mu$ contains a fractal scale. In particular, these measures $\mu$ are not in the Lebesgue class. 
Palle E. T. Jorgensen