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