Summary
Let {X G,G bounded Borel subset of LoRv} be a subadditive spatial process with finite constantγ. It will be proved that as G→∞ (in some sense), the average (1/¦G¦).X G converges in L1, and if in addition the process is strongly subadditive, it converges almost surely towards an invariant random variable with expectationγ.
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Nguyen, X.X. Ergodic theorems for subadditive spatial processes. Z. Wahrscheinlichkeitstheorie verw Gebiete 48, 159–176 (1979). https://doi.org/10.1007/BF01886870
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DOI: https://doi.org/10.1007/BF01886870