We lift important results about universally typical sets, typically sampled sets, and empirical entropy estimation in the theory of samplings of discrete ergodic information sources from the usual one-dimensional discrete-time setting to a multidimensional lattice setting. We use techniques of packings and coverings with multidimensional windows to construct sequences of multidimensional array sets which in the limit build the generated samples of any ergodic source of entropy rate below an $h_{0}$ with probability one and whose cardinality grows at most at exponential rate $h_{0}$.
universal codes, typical sampling sets, entropy estimation, asymptotic equipartition property, ergodic theory
94A24, 62D05, 94A08