© Institute of Mathematical Statistics, 2014 NOISE AS A BOOLEAN ALGEBRA OF σ-FIELDS

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 alge-bra if and only if the noise is classical, which answers an old question of J. Feldman. Introduction. The product of two measure spaces, widely known among mathematicians, leads to the tensor product of the corresponding Hilbert spaces L2. The less widely known product of an infinite sequence of probability spaces leads to the so-called infinite tensor product space. A continuous product of probabil-ity spaces, used in the theory of noises, leads to a continuous tensor product o