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

The Fermionic Entanglement Entropy and Area Law for the Relativistic Dirac Vacuum State