  The Nevanlinna parametrization establishes a bijection between the class of
all measures having a prescribed set of moments and the class of Pick
functions. The fact that all measures constructed through the Nevanlinna
parametrization have identical moments follows from the theory of orthogonal
polynomials and continued fractions. In this paper we explore the opposite
direction: we construct a set of measures and we show that they all have
identical moments, and then we establish a Nevanlinna-type parametrization for
this set of measures. Our construction does not require the theory of
orthogonal polynomials and it exposes the analytic structure behind the
Nevanlinna parametrization.
