  Coherent states (CS) quantum entropy can be split into two components. The
dynamical entropy is linked with the dynamical properties of a quantum system.
The measurement entropy, which tends to zero in the semiclassical limit,
describes the unpredictability induced by the process of a quantum approximate
measurement. We study the CS--measurement entropy for spin coherent states
defined on the sphere discussing different methods dealing with the time limit
$n \to \infty$. In particular we propose an effective technique of computing
the entropy by iterated function systems. The dependence of CS--measurement
entropy on the character of the partition of the phase space is analysed.
