Abstract
If Exc is the set of all excessive measures associated with a submarkovian resolvent on a Lusin measurable space and B is a balayage on Exc then we show that for any m∈Exc there exists a basic set A (determined up to a m-polar set) such that Bξ=(BA)*ξ for any ξ∈ Exc, ξ ≪ m. The m-quasi-Lindelöf property (for the fine topology) holds iff for any B there exists the smallest basic set A as above. We characterize the case when any B is representable i.e. there exists a basic set such that B=(BA)* on Exc.
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Beznea, L., Boboc, N. Balayages on Excessive Measures, their Representation and the Quasi-Lindelöf Property. Potential Analysis 7, 805–824 (1997). https://doi.org/10.1023/A:1008622710481
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DOI: https://doi.org/10.1023/A:1008622710481