Boris Tsirelson,
"Noise as a Boolean algebra of sigma-fields"
arXiv:1111.7270.
Available online (free of charge) from e-print archive (USA):
arXiv.org/abs/1111.7270/
or its Israeli mirror:
il.arXiv.org/abs/1111.7270/

A research eprint, 43 pages, bibl. 20 refs.

The black noise of two-dimensional percolation, disclosed recently by O. Schramm, S. Smirnov and C. Garban, exceeds the limits of the existing framework based on one-dimensional intervals. A remake of the theory of noises, provided here, treats them as Boolean algebras of sigma-fields. Completeness of the Boolean algebra implies classicality, which answers an old question of J. Feldman.

1. Introduction.
1. Main results.
2. Preliminaries.
3. Convergence of sigma-fields and independence.
4. Noise-type completion.
5. Classicality and blackness.
6. The easy part of Theorem 1c2.
7. The difficult part of Theorem 1c2.