I: 07, 163-165, LNM 39 (1967)
MEYER, Paul-André
Sur un théorème de Deny (Potential theory, Measure theory)
In the potential theory of a resolvent which satisfies the absolute continuity hypothesis, every sequence of excessive functions contains a subsequence which converges except on a set of potential zero. It is also proved that a sequence which converges weakly in $L^1$ but not strongly must oscillate around its limit
Comment: a version of this result in classical potential theory was proved by Deny, C.R. Acad. Sci., 218, 1944. The cone of excessive functions possesses good compactness properties, discovered by Mokobodzki. See Dellacherie-Meyer, Probabilités et Potentiel, end of chapter XII
Keywords: A.e. convergence, Subsequences
Nature: Original
Retrieve article from Numdam

---