  An equilibrium statistical system is known to be stable if the fluctuations
of global observables are normal, when their dispersions are proportional to
the number of particles, or to the system volume. A general theorem is
rigorously proved for the case, when an observable is a sum of linearly
independent terms: The dispersion of a global observable is normal if and only
if all partial dispersions of its terms are normal, and it is anomalous if and
only if at least one of the partial dispersions is anomalous. This theorem, in
particular, rules out the possibility that in a stable system with
Bose-Einstein condensate some fluctuations of either condensed or noncondensed
particles could be anomalous. The conclusion is valid for arbitrary systems,
whether uniform or nonuniform, interacting weakly or strongly. The origin of
fictitious fluctuation anomalies, arising in some calculations, is elucidated.
