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Points extrémaux du convexe des mesures majorées par une capacité. (Extreme elements in the convex set of measures majorized by a capacity). (French) Zbl 0777.31009

Summary: Let \(C\) be an alternating capacity of order 2 on a metrizable compact space \(E\), and let \({\mathcal P}_ C\) be the convex set of all measures majorized by \(C\). We describe the set of extreme points of \({\mathcal P}_ C\) when \({\mathcal P}_ C\) consists of all atomic measures or when \(C\) takes a finite number of values. Other results are also considered.

MSC:

31C15 Potentials and capacities on other spaces
28C15 Set functions and measures on topological spaces (regularity of measures, etc.)
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