  The quantitative knowledge of heavy nuclei's partonic structure is currently
limited to rather large values of momentum fraction $x$ -- robust experimental
constraints below $x \sim 10^{-2}$ at low resolution scale $Q^2$ are
particularly scarce. This is in sharp contrast to the free proton's structure
which has been probed in deep inelastic scattering (DIS) measurements down to
$x \sim 10^{-5}$ at perturbative resolution scales. The construction of an
Electron-Ion Collider (EIC) with a possibility to operate with a wide variety
of nuclei, will allow one to explore the low-$x$ region in much greater detail.
In the present paper we simulate the extraction of the nuclear structure
functions from measurements of inclusive and charm reduced cross sections at an
EIC. The potential constraints are studied by analyzing simulated data directly
in a next-to-leading order global fit of nuclear parton distribution functions
based on the recent EPPS16 analysis. A special emphasis is placed on studying
the impact an EIC would have on extracting the nuclear gluon PDF, the partonic
component most prone to non-linear effects at low $Q^2$. In comparison to the
current knowledge, we find that the gluon PDF can be measured at an EIC with
significantly reduced uncertainties.
