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A halo mass function (HMF) is a distribution function (essentially an unnormalized probability density function) mapping mass quantities to the quantity of dark matter halos with that mass. They are of use in cosmology and cosmological simulations.
A sub-halo mass function is such a distribution of sub-halos within a dark matter halo, and a conditional sub-halo mass function is one parameterized by the mass of the particular dark matter halo (analogous to a conditional stellar mass function).
Note that the term mass function used here is not in the sense of a probability mass function (PMF), a function yielding the probability that some discrete random variable takes on a given value.