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Apr 1, 2020 at 23:23 vote accept Sophie M
Mar 31, 2020 at 17:54 answer added R W timeline score: 2
Mar 31, 2020 at 17:53 comment added Sophie M Thanks! It looks like this decomposition may not quite be measurable, but it is universally measurable (in particular, it becomes measurable if you replace $\mathcal{B}$ and $\mathcal{C}$ by their completions with respect to $\mu$ and $\nu$, respectively), which is enough. Universal measurability will actually help elsewhere in this project, too, so I'm glad to have learned about it here.
Mar 31, 2020 at 17:18 comment added Anthony Quas Jisang Yoo's paper: arxiv.org/abs/1612.08648 has a lemma (Lemma 3.1) showing measurability of the decomposition by number of pre-images.
Mar 31, 2020 at 16:19 history asked Sophie M CC BY-SA 4.0