  We employ the machinery of smooth scaling and coarse-graining of observables,
developed recently by us in the context of so-called fluctuation operators
(inspired by prior work of Verbeure et al) to make a rigorous renormalisation
group analysis of the critical regime. The approach appears to be quite
general, encompassing classical, quantum, discrete and continuous systems. One
of our central topics is the analysis of the famous `scaling hypothesis', that
is, we make a general investigation under what conditions on the l-point
correlation functions a scale invariant (non-trivial) limit theory can be
actually attained. Furthermore, we study in a rigorous manner questions like
the quantum character of the system in the scaling limit, the phenomenon of
critical slowing down etc.
