Simple question about Lebesgue and Borel sigma algebra

1. Nov 25, 2007

quasar987

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?

2. Nov 25, 2007

morphism

The empty set!

3. Nov 25, 2007

quasar987

it's the other way around. we want B borel such that N is contained in B

4. Nov 27, 2007

quasar987

bump!

5. Nov 27, 2007

morphism

Oops!

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