Localization of gravity in brane world with arbitrary extra dimensions

We study the induced 4-dimensional linearized Einstein field equations in an m-dimensional bulk space by means of a confining potential. It is shown that in this approach the mass of graviton is quantized. The cosmological constant problem is also addressed within the context of this approach. We show that the difference between the values of the cosmological constant in particle physics and cosmology stems from our measurements in two different scales, small and large.