In generalization of known results, we present rigorous sum rules for inclusive cross sections based upon conservation of momentum or of any additive discrete quantum number. Included are formulas which normalize inclusive cross sections in terms of ${\sigma }_{\mathrm{total}}$ independently of multiplicities. The sum rules could be useful in constraining theoretical models which construct inclusive cross sections without detailed reference to exclusive processes. Some applications are described and a generalization to the tensors governing weak and electromagnetic inclusive reactions is given.

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