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Certain elements of the boundary dependence of minimal harmonic functions in Euclidean domains are considered. For a given minimal harmonic function A on a domain Í2, sets on the boundary of Q or (relative) neighborhoods of such sets are sought wherein the behavior of h determines h in all of ti. The set of determining singletons on the boundary is shown to be connected.doi:10.2307/2041140 fatcat:x4cvy5twfzbulpfpm2r3d7n6je