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The measure of a measurement
Journal article   Peer reviewed

The measure of a measurement

Journal of mathematical physics, Vol.48(10), pp.103506-103506-15
2007
DOI: 10.1063/1.2794561
url
https://arxiv.org/pdf/math-ph/0702054View
Open Access

Abstract

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 < 1 and some s > 1 . We identify these scales s by considering the asymptotic properties of u ( J ) ∕ ∣ J ∣ s where J are dyadic subintervals, and ∣ J ∣ → 0 .

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