Packing topological pressure for amenable group actions

In this paper, we first prove the variational principle for amenable packing topological pressure. Then, we obtain an inequality concerning amenable packing pressure for factor maps. Finally, we show that the amenable packing topological pressure of the set of generic points for any invariant Borel probability measure $ \mu, $ $ P^P(G_\mu,\{F_n\}_{n = 1}^{\infty},f) $ is equal to the sum of the measure-theoretic entropy $ h_\mu(X,G) $ and $ \int f \text{d}\mu $, when the system satisfies the almost specification property, or $ \mu $ is ergodic.