The Annals of Probability

Noise as a Boolean algebra of $\sigma$-fields

Boris Tsirelson

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Abstract

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

Article information

Source
Ann. Probab., Volume 42, Number 1 (2014), 311-353.

Dates
First available in Project Euclid: 9 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.aop/1389278526

Digital Object Identifier
doi:10.1214/13-AOP861

Mathematical Reviews number (MathSciNet)
MR3161487

Zentralblatt MATH identifier
1317.60066

Subjects
Primary: 60G99: None of the above, but in this section
Secondary: 60A10: Probabilistic measure theory {For ergodic theory, see 28Dxx and 60Fxx} 60G20: Generalized stochastic processes 60G60: Random fields

Keywords
Black noise

Citation

Tsirelson, Boris. Noise as a Boolean algebra of $\sigma$-fields. Ann. Probab. 42 (2014), no. 1, 311--353. doi:10.1214/13-AOP861. https://projecteuclid.org/euclid.aop/1389278526


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