A proposed theorem: if the state spaces of distinguishable subsystems are convex sets whose duals admit a product rule, then the dual space of the composite must contain a copy of the tensor product of the subsystem duals.
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On the notion of composite system
A proposed theorem: if the state spaces of distinguishable subsystems are convex sets whose duals admit a product rule, then the dual space of the composite must contain a copy of the tensor product of the subsystem duals.