See this link for a description of the van den Berg-Kesten-Reimer inequality. How important is the assumption that $\Omega_i$ are finite spaces?

When Berg-Kesten state the inequality in their 1985 paper, they state it for product measures on $\mathbb{R}$, but only for increasing events.

Does Reimer's general proof work for all events work without too much effort on infinite spaces with product measure?


1 Answer 1


Check this out, I hope it helps.

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

  • $\begingroup$ I found this paper, after I posted the question :P. Thanks! $\endgroup$
    – arjun
    Commented Feb 1, 2017 at 0:48

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