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Generalized structure of the interaction term of multigravity is analyzed indetail. The coincidence limit of any multigravity theory is defined and thecompatibility equation for the interaction potential is derived which isstudied in the weak perturbation limit of metric. The most general propertiesof the invariant volume and the scalar potential of multigravity areinvestigated. The general formula for multigravity invariant volume using threemeans (arithmetic, geometric and harmonic) is derived. The Pauli-Fierz massterm for bigravity in the weak field limit is obtained.

Coincidence limit and generalized interaction term structure in multigravity