  We prove that there exists uncountably many pairwise disjoint open subsets of
the Gelfand space of the measure algebra on any locally compact non-discrete
abelian group which shows that this space is not separable (in fact, we prove
this assertion for the ideal $M_{0}(G)$ consisting of measures with
Fourier-Stieltjes transforms vanishing at infinity which is a stronger
statement). As a corollary, we obtain that the spectras of elements in the
algebra of measures cannot be recovered from the image of one countable subset
of the Gelfand space under Gelfand transform, common for all elements in the
algebra.
