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We lift important results about universally typical sets, typically sampledsets, and empirical entropy estimation in the theory of samplings of discreteergodic information sources from the usual one-dimensional discrete-timesetting to a multidimensional lattice setting. We use techniques of packingsand coverings with multidimensional windows to construct sequences ofmultidimensional array sets which in the limit build the generated samples ofany ergodic source of entropy rate below an $h_0$ with probability one andwhose cardinality grows at most at exponential rate $h_0$.

Universally Typical Sets for Ergodic Sources of Multidimensional Data