  A new and relatively elementary approach is proposed for solving the problem
of fair division of a continuous resource (measurable space, pie, etc.) between
several participants, the selection criteria of which are described by charges
(signed measures). The setting of the problem with charges is considered for
the first time. The problem comes down to analyzing the properties of the
trajectories of a specially constructed dynamical system acting in the space of
finite measurable partitions. Exponentially fast convergence to a limit
solution is proved for both the case of true measures and the case of charges.
