Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1995-06-30
On Continuous CapacitiesM. Brzezina (1) Universität Erlangen-Nürnberg, Germany
Let $(X, W)$ be a balayage space, $\gamma$ a Choquet capacity on $X$, $\beta(E)$ the essential base of $E \subset X$ and, for a compact set $K \subset X, \alpha (K) = \gamma (\beta(K))$. Then some properties of the set function $\alpha$ are investigated. In particular, it is shown when $\alpha$ is the Choquet capacity. Further, some relation a to the so-called continuous capacity deduced from a kernel on $X$ is given. At last, some open problems from the book  by G. Anger are solved.
Keywords: Capacities, continuous capacities, semipolar sets, essential bases
Brzezina M.: On Continuous Capacities. Z. Anal. Anwend. 14 (1995), 213-224. doi: 10.4171/ZAA/671