Noise as a Boolean algebra of $\sigma$-fields
Probability
2014-01-16 v3
Abstract
A noise is a kind of homomorphism from a Boolean algebra of domains to the lattice of -fields. Leaving aside the homomorphism we examine its image, a Boolean algebra of -fields. The largest extension of such Boolean algebra of -fields, being well-defined always, is a complete Boolean algebra if and only if the noise is classical, which answers an old question of J. Feldman.
Keywords
Cite
@article{arxiv.1111.7270,
title = {Noise as a Boolean algebra of $\sigma$-fields},
author = {Boris Tsirelson},
journal= {arXiv preprint arXiv:1111.7270},
year = {2014}
}
Comments
Published in at http://dx.doi.org/10.1214/13-AOP861 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)