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