Ratio asymptotics of Hermite–Padé polynomials for Nikishin systems

The existence of ratio asymptotics is proved for a sequence of multiple orthogonal polynomials with orthogonality relations distributed among a system of $m$ finite Borel measures with support on a bounded interval of the real line which form a so-called Nikishin system. For $m=1$ this result reduces to Rakhmanov's celebrated theorem on the ratio asymptotics for orthogonal polynomials on the real line.