an approach of randomness of a sample based on its weak ergodic limit

Clicks: 139
ID: 202902
2017
For a Polish Sample Space with a Borel σ-field with a surjective measurable transformation, we define an equivalence relation on sample points according to their ergodic limiting averages. We show that this equivalence relation partitions the subset of sample points on measurable invariant subsets, where each limiting distribution is the unique ergodic probability measure defined on each set. The results obtained suggest some natural objects for the model of a probabilistic time-invariant phenomenon are uniquely ergodic probability spaces. As a consequence of the results gained in this paper, we propose a notion of randomness that is weaker than recent approaches to Schnorr randomness.
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londoo2017journalan Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;Jaime A. Londoño
Journal nature protocols
Year 2017
DOI 10.1155/2017/9139645
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