On Instability of the Ergodic Limit Theorems with Respect to Small Violations of Algorithmic Randomness

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.

arXiv comment32 pages. arXiv admin note: substantial text overlap with arXiv:0806.4572