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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

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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,

Keywords: A.e. convergence, Subsequences

Nature: Original

Retrieve article from Numdam