  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 $h_0$.
