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The inverse Henderson problem of statistical mechanics concerns classicalparticles in continuous space which interact according to a pair potentialdepending on the distance of the particles. Roughly stated, it asks for theinteraction potential given the equilibrium pair correlation function of thesystem. In 1974 Henderson proved that this potential is uniquely determined ina canonical ensemble and he claimed the same result for the thermodynamicallimit of the physical system. Here we provide a rigorous proof of a slightlymore general version of the latter statement using Georgii's version of theGibbs variational principle.

A note on the uniqueness result for the inverse Henderson problem