In this paper, we propose a new approach to singular limits of inviscid fluid\nflows based on the concept of dissipative measure-valued solutions. We show\nthat dissipative measure-valued solutions of the compressible Euler equations\nconverge to the smooth solution of the incompressible Euler system when the\nMach number tends to zero. This holds both for well-prepared and ill-prepared\ninitial data, where in the latter case the presence of acoustic waves causes\ndifficulties. However this effect is eliminated on…