Description:
<jats:p>We identify a fractal scale s in a family of Borel probability measures μ on the unit interval which arises independently in quantum information theory and in wavelet analysis. The scales s we find satisfy s∊R+ and s≠1, some s&lt;1 and some s&gt;1. We identify these scales s by considering the asymptotic properties of u(J)∕∣J∣s where J are dyadic subintervals, and ∣J∣→0.</jats:p>