“…For general compact sets E contained in the complex plane the situation is not quite the same. There are many examples for which Szegő asymptotics takes place for measures supported on a single Jordan curve or arc (see [23,27,34,42,43,44]) and polynomials orthogonal with respect to area type measures on a Jordan region (see [12,26,28,33,35]). Outside of the previously mentioned cases of the segment and the unit circle, the only case fully described and easily verifiable where R(E) is substantially larger than S(E) is when E is an arc of the unit circle, see [3,Theorem 1] and [6,Theorem 1].…”