# Set of Measure zero

A set E subset of real numbers has measure zero. Set A={x2 : x$$\in$$E}. How to prove that set A has measure zero?
(E could be any unbounded subset of R)

I would approximate E by open intervals. That is: there exists open intervals $$]a_i,b_i[$$ such that

$$E\subseteq \bigcup]a_i,b_i[$$

and such that

$$\sum{b_i-a_i}<\epsilon$$.

Now square the open intervals to obtain an approximation of A.

But intervals are not bounded. b2i-a2i does not have a bound when b--ai is bounded.

lavinia