In https://arxiv.org/abs/gr-qc/9210011 on p. 22 the author encounters the Dirac bi-density $\delta(x,x')$ in certain Poisson bracket relations in Hamiltonian mechanics.
He says that $\delta(x,x')$ is a scalar density of weight zero in its first argument and a scalar density of weight one in its second argument. The latter means $f(x)=\int f(x')\delta(x,x')dx'$. But what does the former mean?
[Crossposted to phys.SE]