Comparison of two capacities in \({\mathbb{C}}^ n\) (Q1065207)

There exist several different capacities arising naturally in connection with various problems of the theory of holomorphic and plurisubharmonic functions. The relationship between the capacities is far from being clear. In the paper in question a quantitative relationship between the Bedford-Taylor relative capacity and a capacity defined in terms of Tchebycheff constants is established. The result is shown to be connected with the well known Josefson's theorem on the equivalence of locally and globally pluripolar sets in \({\mathbb{C}}^ n\). Also, a short proof of El Mir's extension of Josefson's theorem is given. For related results see \textit{J. Siciak} [''Extremal plurisubharmonic functions and capacities in \({\mathbb{C}}^ n\)''. (1982)] and \textit{N. Levenberg} and \textit{B. A. Taylor} [''Comparison of capacities in \({\mathbb{C}}^ n\)''. Preprint (1983)].