Extremal problems of potential theory in locally compact spaces (Q2739822)

The problem of the minimum of the energy NEWLINE\[NEWLINE\iint\kappa(x,y)d(\mu\otimes\mu)(x,y),NEWLINE\]NEWLINE where \(\kappa(x,y)\) is a lower semicontinuous function, on the class of Radon measures \(\mu\) on the locally compact space \(X\) is investigated. The author obtains necessary and (or) sufficient conditions for the existence of measures with minimal energy. Potentials of these measures are described.