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The fact that like no probability books mention linear forms forms a travesty https://en.wikipedia.org/wiki/Linear_form https://en.wikipedia.org/wiki/Linear_for

• consilient 3y ago
  Why would they? All of the probability-theoretic structure comes from the fact that a measure is not just an arbitrary one-form, and has lots of extra properties. And then if you want to do probability over arbitrary manifolds, you need to talk about differential forms in general: there's no point at which it makes sense to generalize to one-forms but no further.
• rhymer 3y ago
  Maybe "Probability via Expectation" by Peter Whittle https://link.springer.com/book/10.1007/978-1-4612-0509-8 https://link.springer.com/book/10.1007/978-1-4612-0509-8 or "Infinite Dimensional Analysis" by Charalambos Aliprantis and Kim Border https://link.springer.com/book/10.1007/3-540-29587-9 https://link.springer.com/book/10.1007/3-540-29587-9?