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.


31D05 Axiomatic potential theory
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