  Within the non-relativistic potential scattering theory, we derive a
generalized version of the L\"uscher formula, which includes three-particle
inelastic channels. Faddeev equations in a finite volume are discussed in
detail. It is proved that, even in the presence of the three-particle
intermediate states, the discrete spectrum in a finite box is determined by the
infinite-volume elements of the scattering S-matrix up to corrections,
exponentially suppressed at large volumes.
