Minkowski's measure regularity conjecture

Let $Q$ be Minkowski's question-mark function on $[0,1]$, and let $\b5$ be the singular-continuous measure whose distribution function is $Q$, so that

$$Q(x)=\int_0^x d\mu.$$

Minkowski's measure regularity conjecture. Minkowski's measure $\mu$ is regular in the sense of Ullman--Stahl--Totik. This is a problem in logarithmic potential theory and orthogonal polynomials; the paper gives theoretical arguments and numerical evidence, but no proof is supplied.