The Riemann mapping theorem says that a strict, nonempty open subset of the complex plane is conformally equivalent to the unit disk.

The measurable Riemann mapping theorem asserts the existence and uniqueness of a quasiconformal homeomorphism $f$ satisfying the Beltrami equation: $$\frac{\partial f}{\partial \overline{z}} = \mu(z)\frac{\partial f}{\partial z} $$ for given $\mu$ with $ \lVert\mu\rVert_{\infty}<1$. What (if anything) do these two statements have to do with each other? Wikipedia points out in the link above that the latter isn't a direct generalization of the former, although there does seems to be a proof of Riemann mapping theorem from the measurable RMT.