  We consider the compressible Euler system describing the motion of an ideal
fluid confined to a straight layer
$\Omega_{\delta}=(0,\delta)\times\mathbb{R}^2, \ \ \delta>0$. In the framework
of dissipative measure-valued solutions, we show the convergence to the strong
solution of the 2D incompressible Euler system when the Mach number tends to
zero and $\delta\rightarrow0$.
