  We formulated a problem on hypersonic limit of two-dimensional steady
non-isentropic compressible Euler flows passing a straight wedge. It turns out
that Mach number of the upcoming uniform supersonic flow increases to infinite
may be taken as the adiabatic exponent $\gamma$ of the polytropic gas decreases
to $1$. We proposed a form of the Euler equations which is valid if the
unknowns are measures and constructed a measure solution contains Dirac
measures supported on the surface of the wedge. It is proved that as $\gamma
\to1$, the sequence of solutions of the compressible Euler equations that
containing a shock ahead of the wedge converge vaguely as measures to the
measure solution we constructed. This justified the Newton theory of hypersonic
flow passing obstacles in the case of two-dimensional straight wedges. The
result also demonstrates the necessity of considering general measure solutions
in the studies of boundary-value problems of systems of hyperbolic conservation
laws.
