Boris Tsirelson,
"Noise as a Boolean algebra of sigma-fields. III. An old question of Jacob Feldman"
arXiv:1110.3464.
Available online (free of charge) from e-print archive (USA):
arXiv.org/abs/1110.3464/
or its Israeli mirror:
il.arXiv.org/abs/1110.3464/

A research eprint, 16 pages, bibl. 4 refs.

The noise-type completion C of a noise-type Boolean algebra B is generally not the same as the closure of B. As shown in Part I (Introduction, Theorem 2), C consists of all complemented elements of the closure. It appears that C is the whole closure if and only if B is classical (as defined in Part II, Sect. 1a), which is the main result of this Part III.

1. Introduction.
1. The easy direction.
2. The difficult direction: nonspectral arguments.
3. The difficult direction: spectral arguments.