A lower estimate of the sum of the capacities of condensers
The main result is contained in a theorem asserting the inequality \(\sum^{n}_{k=1}| A_ k| \geq \sum^{n}_{k=1}| C_ k|\), where \(| A_ k|\) is the capacity of the condenser \(A_ k\) with the potential function \(\omega (z,A_ k)\) and \(| C_ k|\) is the capacity of the condenser \(C^ n_ k=\{\dot G^ n_ k,E_{\ell}\}\); \(\dot G^ n_ k\) is the convex component of the set \(G^ n_ k\) in the neighbourhood of \(E_{\ell}\). This inequality could be extended to condensers with compact sets having transfinite diameter.
scientific article; zbMATH DE number 4161086