  The theory of Generalized Locally Toeplitz (GLT) sequences of matrices has
been developed in order to study the asymptotic behaviour of particular
spectral distributions when the dimension of the matrices tends to infinity. A
key concepts in this theory are the notion of Approximating Classes of
Sequences (a.c.s.), and spectral symbols, that lead to define a metric
structure on the space of matrix sequences, and provide a link with the
measurable functions. In this document we prove additional results regarding
theoretical aspects, such as the completeness of the matrix sequences space
with respect to the metric a.c.s., and the identification of the space of GLT
sequences with the space of measurable functions.
