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arXiv · 1111.7270

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.

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Boris Tsirelson. 2011-11-30. Noise as a Boolean algebra of $\sigma$-fields. https://doi.org/10.1214/13-aop861

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