But does doesn’t the money pump result for non-independence rely on continuity? Perhaps I missed something there.
(Of note, this is what happens when I try to pull out a few details which are easy to relate and don’t send entirely the wrong intuition—can’t vouch for accuracy, but at least it seems we can talk about it.)
Actually, I realised you didn’t need continuity at all. See the addendum; if you violate independence, you can be weakly money-pumped even without continuity (though the converse may be false).
But does doesn’t the money pump result for non-independence rely on continuity? Perhaps I missed something there.
(Of note, this is what happens when I try to pull out a few details which are easy to relate and don’t send entirely the wrong intuition—can’t vouch for accuracy, but at least it seems we can talk about it.)
Actually, I realised you didn’t need continuity at all. See the addendum; if you violate independence, you can be weakly money-pumped even without continuity (though the converse may be false).