Abstract
Let u ≥ v be positive superharmonic functions in a general potential-theoretic setting, where these functions have a Choquet-type integral representation by minimal such functions with Choquet charges (i.e. representing measures) μ and ν, respectively. We show that μ ≤ ν on the contact set {u − v = 0} of the δ-superharmonic function u − v, if this set is properly interpreted as the set of those minimal superharmonic functions s which satisfy lim sup T s v/u = 1 for the co-fine neighborhood filter T s associated with s. In the setting of classical potential theory for Laplace's equation this result improves on results obtained by Fuglede in 1992.
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