  Regular variation of a multivariate measure with a Lebesgue density implies
the regular variation of its density provided the density satisfies some
regularity conditions. Unlike the univariate case, the converse also requires
regularity conditions. We extend these arguments to discrete mass functions and
their associated measures using the concept that the the mass function can be
embedded in a continuous density function. We give two different conditions,
monotonicity and convergence on the unit sphere, both of which can make the
discrete function embeddable. Our results are then applied to the preferential
attachment network model, and we conclude that the joint mass function of in-
and out-degree is embeddable and thus regularly varying.
