We show that the Bernoulli conjecture holds for sets with small one-dimensional projections, i.e. any bounded Bernoulli process indexed by such set may be represented as a sum of a uniformly bounded process and a process dominated by a bounded Gaussian process.
"On the boundedness of Bernoulli processes over thin sets." Electron. Commun. Probab. 13 175 - 186, 2008. https://doi.org/10.1214/ECP.v13-1362