Noise as a Boolean algebra of sigma-fields. I. Completion
Probability
2011-07-29 v2
Abstract
Nonclassical noises over the plane (such as the black noise of percolation) consist of sigma-fields corresponding to some planar domains. One can treat less regular domains as limits of more regular domains, thus extending the noise and its set of sigma-fields. The greatest extension is investigated in a new general framework.
Cite
@article{arxiv.1107.3042,
title = {Noise as a Boolean algebra of sigma-fields. I. Completion},
author = {Boris Tsirelson},
journal= {arXiv preprint arXiv:1107.3042},
year = {2011}
}
Comments
16 pages. Version 2: Theorem 2 simplified (both formulation and proof)