Check this out if it helps.
The van den Berg--Kesten--Reimer operator and inequality for infinite spaces, by Arratia-Garibaldi-Hales https://arxiv.org/abs/1508.05337
Check this out if it helps.
The van den Berg--Kesten--Reimer operator and inequality for infinite spaces, by Arratia-Garibaldi-Hales https://arxiv.org/abs/1508.05337