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Contrary to the incompressible case not every measure-valued solution of thecompressible Euler equations can be generated by weak solutions or a vanishingviscosity sequence. In the present paper we give sufficient conditions on anadmissible measure-valued solution of the isentropic Euler system to begenerated by weak solutions. As one of the crucial steps we prove an$L^{\infty}$-variant of Fonseca and M\"uller's characterization result forgenerating $\mathcal{A}$-free Young measures in terms of potential operators.More concrete versions of our results are presented in the case of a solutionconsisting of two Dirac measures. We conclude by discussing also necessaryconditions for generating a measure-valued solution by weak solutions or avanishing viscosity sequence and will point out that the resulting gap mainlyresults from obtaining only uniform $L^p$-bounds for $1<p<\infty$ instead of$p=\infty$.

Which measure-valued solutions of the monoatomic gas equations are generated by weak solutions?