  Generalized structure of the interaction term of multigravity is analyzed in
detail. The coincidence limit of any multigravity theory is defined and the
compatibility equation for the interaction potential is derived which is
studied in the weak perturbation limit of metric. The most general properties
of the invariant volume and the scalar potential of multigravity are
investigated. The general formula for multigravity invariant volume using three
means (arithmetic, geometric and harmonic) is derived. The Pauli-Fierz mass
term for bigravity in the weak field limit is obtained.
