Originally Posted by

**davidmccormick** 1. Suppose $\displaystyle A$ is a bounded set and that $\displaystyle m^{*}(

A\cap I)\leq am^{*}(I) $ for every interval I and $\displaystyle 0 < a < 1$. Prove that $\displaystyle m^{*}(A)=0$. What if A is unbounded?

2. $\displaystyle A$ is a subset of $\displaystyle \mathbb{R}$ with the following property: for every $\displaystyle \epsilon > 0$ there exist measurable sets B and C such that :

$\displaystyle B \subset A \subset C$ and $\displaystyle m(c \cap B^c) < \epsilon$. Prove that A is measurable.

thanks.