Noise as a boolean algebra of σ-fields

Boris Tsirelson*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish
Pages (from-to)311-353
Number of pages43
JournalAnnals of Probability
Issue number1
StatePublished - Jan 2014


  • Black noise


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