Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Does anyone have a good proof of Littlewood's first principle?

Let $E$ be a measurable subset of $\mathbb{R}$ of finite measure, and let $\epsilon > 0$. Can anyone provide a rigorous proof that there is an open set $O$ which is the union of a finite number of pairwise disjoint open bounded intervals such that $m(O \setminus E) + m(E \setminus O) < \epsilon$.

Any references or answers would be greatly appreciated!

share|cite|improve this question
See here for some thoughts. – leo May 13 '12 at 0:47

There is a proof in this PDF.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.