  For fitness preferential attachment random networks, we define the empirical
degree and pair measure, which counts the number of vertices of a given degree
and the number of edges with given fits, and the sample path empirical degree
distribution. For the empirical degree and pair distribution for the fitness
preferential attachment random networks, we find a large deviation upper bound.
From this result we obtain a weak law of large numbers for the empirical degree
and pair distribution, and the basic information theorem or an asymptotic
equipartition property for fitness preferential attachment random networks.
