  Generalized multiresolution analyses are increasing sequences of subspaces of
a Hilbert space $\H$ that fail to be multiresolution analyses in the sense of
wavelet theory because the core subspace does not have an orthonormal basis
generated by a fixed scaling function. Previous authors have studied a
multiplicity function $m$ which, loosely speaking, measures the failure of the
GMRA to be an MRA. When the Hilbert space $\H$ is $L^2(\mathbb R^n)$, the
possible multiplicity functions have been characterized by Baggett and Merrill.
Here we start with a function $m$ satisfying a consistency condition which is
known to be necessary, and build a GMRA in an abstract Hilbert space with
multiplicity function $m$.
