Well, when I wrote that I was just inferring it from the article, which while it doesn't explicitly say that they are, is written in a way so as to clearly sugg

Well, when I wrote that I was just inferring it from the article, which while it doesn't explicitly say that they are, is written in a way so as to clearly suggest that they are. But you're right that it doesn't eplicitly say that, now that I look again. But if you click on the link to the actual paper, it says right in the abstract that they're Borel, so yes, they are indeed measurable.