  We study the effects of a generalized uncertainty principle on the classical
and quantum cosmology of a closed Friedmann Universe whose matter content is
either a dust or a radiation fluid. More concretely, assuming the existence of
a minimal length, we show that the entropy will constitute a Dirac observable.
In addition, 't Hooft conjecture on the cosmological holographic principle is
also investigated. We describe how this holographic principle is satisfied for
large values of a quantum number, $n$. This occurs when the entropy is computed
in terms of the minimal area.
