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January 2014 Noise as a Boolean algebra of $\sigma$-fields
Boris Tsirelson
Ann. Probab. 42(1): 311-353 (January 2014). DOI: 10.1214/13-AOP861


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.


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Boris Tsirelson. "Noise as a Boolean algebra of $\sigma$-fields." Ann. Probab. 42 (1) 311 - 353, January 2014.


Published: January 2014
First available in Project Euclid: 9 January 2014

zbMATH: 1317.60066
MathSciNet: MR3161487
Digital Object Identifier: 10.1214/13-AOP861

Primary: 60G99
Secondary: 60A10 , 60G20 , 60G60

Keywords: Black noise

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.42 • No. 1 • January 2014
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