The quantitative knowledge of heavy nucleis 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 protons 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.
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