  We consider the fermionic entanglement entropy for the free Dirac field in a
bounded spatial region of Minkowski spacetime. In order to make the system
ultraviolet finite, a regularization is introduced. An area law is proven in
the limiting cases where the volume tends to infinity and/or the regularization
length tends to zero. The technical core of the paper is to generalize a
theorem of Harold Widom to pseudo-differential operators whose principal
symbols develop a specific discontinuity at a single point.
