  We develop a method to compute effectively the Young measures associated to
sequences of numerical solutions of the compressible Euler system. Our approach
is based on the concept of $\mathcal{K}$-convergence adapted to sequences of
parametrized measures. The convergence is strong in space and time
(a.e.~pointwise or in certain $L^q$ spaces) whereas the measures converge
narrowly or in the Wasserstein distance to the corresponding limit.
