Counterexamples: Integral over the interior of a bounded set
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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
asked Nov 20 at 15:27
B. Pasternak
1,131720
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up vote
0
down vote
favorite
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
asked Nov 20 at 15:27
B. Pasternak
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 at 15:30
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
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
asked Nov 20 at 15:27
B. Pasternak
1,131720
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
asked Nov 20 at 15:27
B. Pasternak
1,131720
asked Nov 20 at 15:27
B. Pasternak
1,131720
asked Nov 20 at 15:27
B. Pasternak
1,131720
asked Nov 20 at 15:27
B. Pasternak
1,131720
asked Nov 20 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 at 15:30
add a comment |
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 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 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 at 15:30
add a comment |
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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 at 15:30