  In various areas of modern physics and in particular in quantum gravity or
foundational space-time physics it is of great importance to be in the
possession of a systematic procedure by which a macroscopic or continuum limit
can be constructed from a more primordial and basically discrete underlying
substratum, which may behave in a quite erratic and irregular way. We develop
such a framework within the category of general metric spaces by combining
recent work of our own and ingeneous ideas of Gromov et al, developed in pure
mathematics. A central role is played by two core concepts. For one, the notion
of intrinsic scaling dimension of a (discrete) space or, in mathematical terms,
the growth degree of a metric space at infinity, on the other hand, the concept
of a metrical distance between general metric spaces and an appropriate scaling
limit (called by us a geometric renormalisation group) performed in this metric
space of spaces. In doing this we prove a variety of physically interesting
results about the nature of this limit process, properties of the limit space
as e.g. what preconditions qualify it as a smooth classical space-time and, in
particular, its dimension.
