On Continuous Capacities

  • M. Brzezina

    Universität Erlangen-Nürnberg, Germany


Let (X,W)(X, W) be a balayage space, γ\gamma a Choquet capacity on XX, β(E)\beta(E) the essential base of EXE \subset X and, for a compact set KX,α(K)=γ(β(K))K \subset X, \alpha (K) = \gamma (\beta(K)). Then some properties of the set function α\alpha are investigated. In particular, it is shown when α\alpha is the Choquet capacity. Further, some relation a to the so-called continuous capacity deduced from a kernel on XX is given. At last, some open problems from the book [1] by G. Anger are solved.

Cite this article

M. Brzezina, On Continuous Capacities. Z. Anal. Anwend. 14 (1995), no. 2, pp. 213–224

DOI 10.4171/ZAA/671