On Instability of the Ergodic Limit Theorems with Respect to Small Violations of Algorithmic Randomness
Information Theory
2012-07-26 v2 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.
Keywords
Cite
@article{arxiv.1105.4274,
title = {On Instability of the Ergodic Limit Theorems with Respect to Small Violations of Algorithmic Randomness},
author = {Vladimir V'yugin},
journal= {arXiv preprint arXiv:1105.4274},
year = {2012}
}
Comments
32 pages. arXiv admin note: substantial text overlap with arXiv:0806.4572