  The Lund Area Law describes the probability for the production of a set of
colourless hadrons from an initial set of partons, in the Lund string
fragmentation model. In this paper we will present a general method to
implement the Area Law for a multi-gluon string state. The partonic states are
in general given by a perturbative QCD cascade and are consequently defined
only down to a cutoff in the energy momentum fluctuations. We will show that
our method defines the states down to the hadronic mass scale inside an
analytically calculable scenario.
  We will then show that there is a differential version of our process which
is closely related to the generalised rapidity range \lambda, which has been
used as a measure on the partonic states. We identify \lambda as the area
spanned between the directrix curve (the curve given by the parton energy
momentum vectors laid out in colour order, which determines the string surface)
and the average curve (to be called the P-curve) of the stochastic X-curves
(curves obtained when the hadronic energy-momentum vectors are laid out in rank
order). Finally we show that from the X-curve corresponding to a particular
stochastic fragmentation situation it is possible to reproduce the directrix
curve (up to one starting vector and a set of sign choices, one for each
hadron).
