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Zeitschrift für Analysis und ihre Anwendungen

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Volume 14, Issue 2, 1995, pp. 213–224
DOI: 10.4171/ZAA/671

Published online: 1995-06-30

On Continuous Capacities

M. Brzezina[1]

(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 [1] 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