Noise as a Boolean algebra of sigma-fields

Details Noise as a Boolean algebra of sigma-fields Noise as a Boolean algebra of sigma-fields

2011-11-30

arxiv.org/abs/1111.7270v1

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43 pages. The former Parts I (arXiv:1107.3042), II (arXiv:1109.1690), III (arXiv:1110.3464) united and redesigned

Scientific paper

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.

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