Noise as a Boolean algebra of sigma-fields. I. Completion
arXiv:1107.3042
Abstract
Nonclassical noises over the plane (such as the black noise of percolation) consist of sigma-fields corresponding to some planar domains. One can treat less regular domains as limits of more regular domains, thus extending the noise and its set of sigma-fields. The greatest extension is investigated in a new general framework.
16 pages. Version 2: Theorem 2 simplified (both formulation and proof)