The main purpose is to generalize a theorem of Arendt about uniqueness of
C0-semigroups from Banach space setting to the general locally convex vector
spaces, more precisely, we show that cores are the only domains of uniqueness
for C0-semigroups on locally convex spaces. As an application, we find a
necessary and sufficient condition for that the mass transport equation has one
unique L1(Rd,dx) weak solution