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Jul 20, 2010 at 22:23 comment added T.. re: "this can even be a proof" --- the results from logic don't quite show that a reasonably defined $f$ has a proof (in the system that defined it) of its Lebesgue measurability. They do show consistency of $f$ being measurable, and that there are natural axioms that, when added to the system, provide a universal proof (not referring to the construction details of any specific $f$) that any reasonable function is measurable.
Jul 20, 2010 at 21:35 history answered Nate Eldredge CC BY-SA 2.5