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We obtain an existence result for a Measure Differential Equation with anadditional nonlinear growth/decay term that may change the sign. The proofrequires a modification of approximating schemes proposed by Piccoli and Rossi.The new scheme combines model discretisation with the exponential solution ofthe nonlinear growth/decay and hence preserves nonnegativity of the measure.Furthermore, we formulate a simpler analytic condition on the Measure VectorField which substantially simplifies the previous proof of continuity ofsolutions with respect to initial data.

Measure Differential Equation with a Nonlinear Growth/Decay Term