A relation between sigma-additivity and linearizability, conjectured by Jacob Feldman in 1971 for continuous products of probability spaces, is established by relating both notions to a recent idea of noise stability/sensitivity.
@article{arxiv.math/9907011,
title = {Noise sensitivity on continuous products: an answer to an old question of J. Feldman},
author = {Boris Tsirelson},
journal= {arXiv preprint arXiv:math/9907011},
year = {2007}
}