  We study sequences of functions of the form F_p^n -> {0,1} for varying n, and
define a notion of convergence based on the induced distributions from
restricting the functions to a random affine subspace. Using a decomposition
theorem and a recently proven equi-distribution theorem from higher order
Fourier analysis, we prove that the limits of such convergent sequences can be
represented by certain measurable functions. We are also able to show that
every such limit object arises as the limit of some sequence of functions.
These results are in the spirit of similar results which have been developed
for limits of graph sequences. A more general, albeit substantially more
sophisticated, limit object was recently constructed by Szegedy in [Sze10].
