### A version of the fundamental theorem of algebra for Markov functions and a generalization of Markov's theorem.

We consider the wide class of Nikishin systems of functions. Such systems are made up of Cauchy transforms

of measures (with a special structure) supported on the same interval. We show that generalized

polynomials made up of polynomial combinations of the functions in the Nikishin system verify a version

of the fundamental theorem of algebra. This result has multiple applications in the asymptotic theory of

multiple orthogonal polynomials and in the convergence theory of Hermite-Pade approximation. In particular,

we give very general conditions under which the sequence of type II Hermite-Pade approximations

of a Nikishin system of functions converges uniformly on each compact subset of the complement of the

interval supporting the measures.

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