  In this work, we prove the convergence of residual distribution schemes to
dissipative weak solutions of the Euler equations. We need to guarantee that
the residual distribution schemes are fulfilling the underlying structure
preserving properties such as positivity of density and internal energy.
Consequently, the residual distribution schemes lead to a consistent and stable
approximation of the Euler equations. Our result can be seen as a
generalization of the Lax-Richtmyer equivalence theorem to nonlinear problems
that consistency plus stability is equivalent to convergence.
