  We show that a free Dirac quantum field on a globally hyperbolic spacetime
has the following structural properties: (a) any two quasifree Hadamard states
on the algebra of free Dirac fields are locally quasiequivalent; (b) the
split-property holds in the representation of any quasifree Hadamard state; (c)
if the underlying spacetime is static, then the nuclearity condition is
satisfied, that is, the free energy associated with a finitely extended
subsystem (``box'') has a linear dependence on the volume of the box and goes
like $\propto T^{s+1}$ for large temperatures $T$, where $s+1$ is the number of
dimensions of the spacetime.
