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The top quark discovered in 1995 at the Fermilab Tevatron Collider is the heaviest known elementary particle. The precise knowledge of its mass yields important constraints on the mass of the yet-undiscovered Higgs boson and allows to probe for physics beyond the Standard Model.§With an excellent adaption of a novel measurement technique described and applied for the first time here, the sensitivity to the top quark mass in the dilepton final state at the D0 experiment could have been improved by more than 30%. Moreover, an extension to the method is presented which allows future measurements to reduce the main limiting systematic uncertainty significantly.