## B. Tsirelson | ## Noise as a Boolean algebra of sigma-fields | ## Recent works |

Boris Tsirelson,

"Noise as a Boolean algebra of σ-fields"

The Annals of Probability **42**:1, 311-353 (2014).

Available online via Project Euclid (not free, sorry):

http://dx.doi.org/10.1214/13-AOP861

or from my site:
[download]

See also
arXiv.org/abs/1111.7270/

A long (42 pages) research paper. Bibl. 22 refs.

A noise is a kind of homomorphism from a Boolean algebra of domains to the lattice of σ-fields. Leaving aside the homomorphism we examine its image, a Boolean algebra of σ-fields. The largest extension of such Boolean algebra of σ-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.

- Introduction.
- Main results.
- Preliminaries.
- Convergence of sigma-fields and independence.
- Noise-type completion.
- Classicality and blackness.
- The easy part of Theorem 1.5.
- The difficult part of Theorem 1.5.

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