pg. 239

[alextzik]

Shouldn't the supremum in equation (13.1) be over the hyperrectangle sets within the set S whose discrepancy we are computing? In other words, H should be constrained within the set S. This would make the last sentence of the section more clear also (S being a non-rectangular set). In addition, given that H is a hyperrectangle set, the expression "where H merely approaches a particular rectangular subset" should be referring to S, right?

[tawheeler]

You are not wrong, but given the context we originally wanted to keep things simple and avoid defining yet another variable (S). Here we can safely assume that the reader understands that H only consists of subsets of our target set.

@mykelk Do you agree?

[mykelk]

Agreed.