There exist a calculation about electromagnetic mass: $$m_\mathrm{em} = \int {1\over 2}E^2 \, dV = \int\limits_{r_e}^\infty \frac{1}{2} \left( {q\over 4\pi r^2} \right)^2 4\pi r^2 \, dr = {q^2 \over 8\pi r_e}$$
Reducing $r_e$ we get infinite mass. It seems to me that the expression $\int {1\over 2}E^2 \, dV$ is infinite too for infinite volume V. Please refute or confirm.