Lagrangian multiform structure for the lattice KP system

We present a Lagrangian for the bilinear discrete KP (or Hirota-Miwa) equation. Furthermore, we show that this Lagrangian can be extended to a Lagrangian 3-form when embedded in a higher dimensional lattice, obeying a closure relation. Thus we establish the multiform structure as proposed in arXiv:0903.4086v1 [nlin.SI] in a higher dimensional case.