  Cosmological perturbations in the brane-world cosmology with a positive
tension brane in the AdS background bulk geometry is analyzed by using the
doubly gauge-invariant formalism. We derive four independent equations for
scalar perturbations in the plane symmetric (K=0) background. Three of these
equations are differential equations written in terms of gauge invariant
variables on the brane only, and another of them is an integro-differential
equation whose kernel is constructed formally from the Z_2-symmetric retarded
Green's function of the bulk gravitational waves. We compare these four
equations with the corresponding equations in the standard cosmology. As a
by-product, we also obtain a set of equations which may be useful in numerical
calculations.
