  This paper presents the derivation of SPH from principles of continuum
mechanics via a measure-based formu- lation. Additionally, it discusses a
theoretical convergence result, the extensions achieved from previous works and
the current limitations of the proof. In support of the theoretical result,
numerical experiments show that SPH converges with respect to the Wasserstein
distance as the number of particles grows to infinity. Convergence is still
observed for those numerical experiments which are not covered by the
hypotheses of the theoretical result. The latter finding suggests that it
should be possible to prove the theoretical result under weaker conditions.
