Mutual energy

Summary

The mutual energy of two positive measures is the double integral of a potential-theoretic kernel against one measure in each variable. It is the interaction energy of two charge distributions, and it equals the integral of the potential of one measure against the other. The energy of a measure is the mutual energy of the measure with itself. So the mutual energy is the bilinear form whose quadratic form is the energy. Its positive definiteness turns measures of finite energy into a pre-Hilbert space, which is the basis of the energy method in potential theory.