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