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Ahlfors and Bers in the introduction of their paper claim that Morrey proved the theorem first, in the case of measurable mu. So the attribution to Ahlfors and Bers of the theorem, as it is stated in the present version of the Wikipedia article (oct 26th 2012) is wrong. I was told that the advantage of the proof by Ahlfors and Bers using singular integral operators is to get continuous/differentiable/holomorphic dependence of the solution w.r.t. the data μ.
Arnaud Chéritat. — Preceding unsigned comment added by 130.120.80.60 (talk) 07:59, 26 October 2012 (UTC)