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Hi, I am so rusty. Is it true that a subset of Euclidean n-space has empty interior if and only if it has (n-space) measure zero? Thanks Rich 11:07, 3 October 2006 (UTC)
- Do you mean Lebesgue measure? If so, then no. A cube from which rational points were taken out has an empty interior but positive measure. But the "if" part is true. -- Meni Rosenfeld ( talk) 12:17, 3 October 2006 (UTC)
- Cool. Is it possible to say what value that measure takes? - 130.237.48.27 12:26, 3 October 2006 (UTC)
- Can you be more specific? In my example, it is the same as that of the original cube. Adding or removing countably many points does not change the Lebesgue measure. -- Meni Rosenfeld ( talk) 12:32, 3 October 2006 (UTC)
- (I was 130.237.48.27 for a brief moment.) Ah, you have already answered my question, thank you. — Bromskloss 13:51, 3 October 2006 (UTC)
Mine as well thanks. Yeah I meant Lebesgue. Rich 16:26, 3 October 2006 (UTC)
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| The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions at one of the pages linked to above. | ||||||||
Hi, I am so rusty. Is it true that a subset of Euclidean n-space has empty interior if and only if it has (n-space) measure zero? Thanks Rich 11:07, 3 October 2006 (UTC)
- Do you mean Lebesgue measure? If so, then no. A cube from which rational points were taken out has an empty interior but positive measure. But the "if" part is true. -- Meni Rosenfeld ( talk) 12:17, 3 October 2006 (UTC)
- Cool. Is it possible to say what value that measure takes? - 130.237.48.27 12:26, 3 October 2006 (UTC)
- Can you be more specific? In my example, it is the same as that of the original cube. Adding or removing countably many points does not change the Lebesgue measure. -- Meni Rosenfeld ( talk) 12:32, 3 October 2006 (UTC)
- (I was 130.237.48.27 for a brief moment.) Ah, you have already answered my question, thank you. — Bromskloss 13:51, 3 October 2006 (UTC)
Mine as well thanks. Yeah I meant Lebesgue. Rich 16:26, 3 October 2006 (UTC)