Counterexamples: Integral over the interior of a bounded set












0














This is basically this question:



Function integrable over the interior but not over the set



I was wondering: is there an easier counterexample that does not involve an obese Cantor set?






integration measure-theory lebesgue-integral







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  • You need a set with relatively large boundary (i.e. positive measure). So a fat Cantor set is about as simple as it can get, I think.
    – Arthur
    Nov 20 '18 at 15:30


















0














This is basically this question:



Function integrable over the interior but not over the set



I was wondering: is there an easier counterexample that does not involve an obese Cantor set?






integration measure-theory lebesgue-integral







share|cite|improve this question






















  • You need a set with relatively large boundary (i.e. positive measure). So a fat Cantor set is about as simple as it can get, I think.
    – Arthur
    Nov 20 '18 at 15:30
















0












0








0







This is basically this question:



Function integrable over the interior but not over the set



I was wondering: is there an easier counterexample that does not involve an obese Cantor set?






integration measure-theory lebesgue-integral







share|cite|improve this question













This is basically this question:



Function integrable over the interior but not over the set



I was wondering: is there an easier counterexample that does not involve an obese Cantor set?






integration measure-theory lebesgue-integral




integration measure-theory lebesgue-integral






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Nov 20 '18 at 15:27









B. Pasternak

1,131720




1,131720












  • You need a set with relatively large boundary (i.e. positive measure). So a fat Cantor set is about as simple as it can get, I think.
    – Arthur
    Nov 20 '18 at 15:30




















  • You need a set with relatively large boundary (i.e. positive measure). So a fat Cantor set is about as simple as it can get, I think.
    – Arthur
    Nov 20 '18 at 15:30


















You need a set with relatively large boundary (i.e. positive measure). So a fat Cantor set is about as simple as it can get, I think.
– Arthur
Nov 20 '18 at 15:30






You need a set with relatively large boundary (i.e. positive measure). So a fat Cantor set is about as simple as it can get, I think.
– Arthur
Nov 20 '18 at 15:30












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