You define the density function of the shell using a direct Delta function and the derivative of a direct Delta function. That means that on the shelf the densi

You define the density function of the shell using a direct Delta function and the derivative of a direct Delta function. That means that on the shelf the density doesn't take any real value. But we can formally integrate Delta functions and their derivatives. When we perform the mass integral we end up with the result m = 0. It's an artifact caused by allowing generalized functions as our density functions A problem is that we don't know how to physically interpret a distribution as a density function. Mass distributions caused by matter all have positive real valued functions as density functions. So if we have these structures in the universe, their cause is probably not physical matter! It would be as if god put his thumb on the scale, and his finger print indented a concentric series of shells where the mass density goes completely nonphysical.