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In this paper, we propose a new approach to singular limits of inviscid fluidflows based on the concept of dissipative measure-valued solutions. We showthat dissipative measure-valued solutions of the compressible Euler equationsconverge to the smooth solution of the incompressible Euler system when theMach number tends to zero. This holds both for well-prepared and ill-preparedinitial data, where in the latter case the presence of acoustic waves causesdifficulties. However this effect is eliminated on unbounded domains thanks todispersion.

On the low Mach number limit for the compressible Euler system