  The unique-continuation property from sets of positive measure is here proven
for the many-body magnetic Schr\"odinger equation. This property guarantees
that if a solution of the Schr\"odinger equation vanishes on a set of positive
measure, then it is identically zero. We explicitly consider potentials written
as sums of either one-body or two-body functions, typical for Hamiltonians in
many-body quantum mechanics. As a special case, we are able to treat atomic and
molecular Hamiltonians. The unique-continuation property plays an important
role in density-functional theories, which underpins its relevance in quantum
chemistry.
