  In the second part of our work on observables we have shown that quantum
observables in the sense of von Neumann, i.e.bounded selfadjoint operators in
some von Neumann subalgebra $R$ of $L(H)$, can be represented as bounded
continuous functions on the Stone spectrum $Q(R)$ of $R$. Moreover, we have
shown that this representation is linear if and only if $R$ is abelian, and
that in this case it coincides with the Gelfand transformation of $R$. In this
part we discuss classical observables, i.e. measurable and continuous
functions, under the same point of view. We obtain results that are quite
similar to the quantum case, thus showing up the common structural features of
quantum and classical observables.
