Condensers with infinitely many touching Borel plates and minimum energy problems

Defining a condenser in a locally compact space as a locally finite, countable collection of Borel sets Aᵢ, i∈ I, with the sign sᵢ=± 1 prescribed such that Aᵢ∩ Aⱼ= whenever sᵢsⱼ=-1, we consider a minimum energy problem w