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Jan 12, 2015 at 15:56 comment added GraduateStudent That was a natural choice, or measurable maps that don't increase measure. It is okay if the Caratheodory construction gives back the completion. Going through a forgetful functor and back through its left adjoint is rarely the identity, and through a right adjoint doesn't have to be either.
Jan 11, 2015 at 11:01 comment added Jochen Wengenroth What about the measurable and measure preserving maps as morphisms? The Caratheodory construction does not really give back the the measure space $(X,\mathscr F,\mu)$ but its completion.
Jan 10, 2015 at 14:27 review Close votes
Jan 13, 2015 at 7:39
Jan 10, 2015 at 13:50 review First posts
Jan 10, 2015 at 14:03
Jan 10, 2015 at 13:49 history asked GraduateStudent CC BY-SA 3.0