Let $ \left\{ {r_i } \right\}_{i = 1}^\infty = \mathbb{Q}$ an enumeration of $\mathbb{Q}$. Let $ J_{n,i} = \left( {r_i - \frac{1} {{2^{n + i} }},r_i + \frac{1} {{2^{n + i} }}} \right) $ $ \forall \left( {n,i} \right) \in {\Bbb N}^2 $ Then define $ A_n = \bigcup\limits_{i \in {\Bbb N}} {J_{n,i} } $ and $ A = \bigcap\limits_{n \in {\Bbb N}} {A_n } $
i) Prove that A has measure zero ii) prove that A cannot be writted as a countable union of sets with null jordan content, where the null jordan content, is the same definition as null measure, only instead of covering with countable intervals, only done with finite, i.e given any $ \varepsilon > 0 $ there exist finite intervals, such that cover the set, and the sum of the lengths, is less than $ \varepsilon > 0 $
Sorry for ask this question, but I want to see an example