Possible Duplicate:
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?
Possible Duplicate:
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?