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Limits of balayage measures. (English) Zbl 1081.31504
Summary: Let $$A$$ be a subset of a balayage space $$(X,W)$$ and $$\nu$$ a measure on $$X$$. It is shown that for every sequence $$\nu_n$$ of measures such that $$\lim_{n\to \infty}\nu_n$$ and $$\lim_{n\to\infty}\nu_n^A = \lambda$$ the limit measure $$\lambda$$ is of the form $$\nu+[(1-f)]^A$$ for some (unique) Borel function $$0\leq f\leq 1_{Cb(A)}$$. Furthermore, conditions are given such that any such function $$f$$ occurs.
##### MSC:
 31D05 Axiomatic potential theory
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##### References:
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