  Generalized Friedmann equations governing the cosmological evolution inside a
thick brane embedded in a five-dimensional Anti-de Sitter spacetime are
derived. These equations are written in terms of four-dimensional effective
brane quantities obtained by integrating, along the fifth dimension, over the
brane thickness. In the case of a Randall-Sundrum type cosmology, different
limits of these effective quantities are considered yielding cosmological
equations which interpolate between the thin brane limit (governed by
unconventional brane cosmology), and the opposite limit of an ``infinite''
brane thickness corresponding to the familiar Kaluza-Klein approach. In the
more restrictive case of a Minkowski bulk, it is shown that no effective
four-dimensional reduction is possible in the regimes where the brane thickness
is not small enough.
