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Oct 15, 2019 at 12:54 comment added yada Very interesting. For a Galois connection we require partial orders on the collection of positive measures and the collection of outer measures. Do you have an idea which partial order to choose, so that the fixed points of the Galois connection are precisely the "Caratheodory complete" measures (i.e. complete and defined on the $\sigma$-algebra of Caratheodory measurable sets) and the regular outer measures?
Jun 22, 2012 at 16:41 vote accept Bruce
Jun 22, 2012 at 16:41 comment added Bruce Thank you; excellent answer! Your suggestions give me a ot to think about, and Fremlin's volume 4 seems very much along the lines I was hoping for, and then some.
Jun 22, 2012 at 10:00 history answered user24527 CC BY-SA 3.0