  We provide an interpretation of the structure functions of a thermal medium
such as the quark-gluon plasma in terms of the scattering of an incoming
electron on the medium via the exchange of a spacelike photon. We then focus on
the deep-inelastic scattering (DIS) regime, and formulate the corresponding
moment sum rules obeyed by the structure functions. Accordingly, these moments
are given by the thermal expectation value of twist-two operators, which is
computable from first principles in lattice QCD for the first few moments. We
also show how lattice QCD calculations can be used to probe how large the
photon virtuality needs to be in order for the Bjorken scaling of structure
functions to set in. Finally, we provide the parton-model interpretation of the
structure functions in the Bjorken limit and test its consistency. As in DIS on
the proton, the kinematic variable $x$ is proportional to the longitudinal
momentum carried by the partons, however $x$ ranges from zero to infinity.
Choosing the parton momentum parametrization to be $ x T u$ where $u$ is the
fluid four-velocity and $T$ its temperature in the rest frame, the parton
distribution function for a plasma of non-interacting quarks is proportional to
$ x \log(1+e^{-x/2}) $.
