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On Instability of the Ergodic Limit Theorems with Respect to Small Violations of Algorithmic Randomness (1105.4274v2)
Published 21 May 2011 in cs.IT and math.IT
Abstract: An instability property of the Birkhoff's ergodic theorem and related asymptotic laws with respect to small violations of algorithmic randomness is studied. The Shannon--McMillan--Breiman theorem and all universal compression schemes are also among them.