Simple question about Lebesgue and Borel sigma algebra

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The discussion centers on the relationship between null Lebesgue measure sets and Borel sets. It establishes that if a set N has null Lebesgue measure, it is indeed possible to find a Borel set B that contains N and also has null measure. This conclusion is supported by the property of regularity of Lebesgue measure, which allows for such containment. The participants clarify the direction of containment, emphasizing that N is contained within B.

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If N is of null Lebesgue measure. Can we find a Borel set B of null measure such that N is entirely contained in B?
 
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The empty set!
 
it's the other way around. we want B borel such that N is contained in B
 
bump!
 
quasar987 said:
it's the other way around. we want B borel such that N is contained in B
Oops!

This is also true. It follows from the fact that the Lebesgue measure is regular.
 

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