Measure of the boundary of an open set of finite measure

Asked Aug 24 '12 at 09:33

Active Aug 29 '12 at 18:21

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Comparing the Lebesgue measure of an open set and its closure

Given an open set in $\Bbb R^2$ of finite Lebesgue measure, why does the boundary of its closure have measure zero?

edited Apr 13 '17 at 12:20

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asked Aug 24 '12 at 09:33

corni75

4

This is false, isn't it? Consider the inside of a positive-measure Jordan curve. – Chris Eagle Aug 24 '12 at 09:53
4

You can take a look at here : http://mathoverflow.net/questions/25993/sets-with-positive-lebesgue-measure-boundary. – Ahriman Aug 24 '12 at 09:53
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Or here. – Did Aug 24 '12 at 10:04

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