  We analyze cosmological equations in the brane world scenario with one extra
space-like dimension. We demonstrate that the cosmological equations can be
reduced to the usual 4D Friedmann type if the bulk energy-momentum tensor is
different from zero. We then generalize these equations to the case of a brane
of finite thickness. We also demonstrate that when the bulk energy-momentum
tensor is different from zero, the extra space-like dimension can be
compactified with a single brane and show that the stability of the radius of
compactification implies standard cosmology and vice versa. For a brane of
finite thickness, we provide a solution such that the 4D Planck scale is
related to the fundamental scale by the thickness of the brane. In this case,
compactification of the extra dimension is unnecessary.
