  In this article we construct a canonical K\"{a}hler-Einstein current on a LC
(log canonical) pairs of log general type as the limit of a sequence of
canonical K\"{a}hler-Einstein currents on KLT(Kawamata log terminal) pairs of
log general type. We call the volume form associated with the canonical
K\"{a}hler-Einstein current the canonical measure of the LC pair. We prove that
the relative canonical measure on a projective family of LC pairs of log
general type defines a singular hermitian metric on the relative log canonical
bundle and the metric has semipositive curvature in the sense of current. This
is the first semipositivity result for relative log canonical bundles of a
family of LC pairs in general dimension.
  Our proof depends on certain Ricci iterations and dynamical systems of
Bergman kernels.
