Proving X is a Set of Measure 0 with Infinite Sequence of Balls

[Riam]

Please I need your help in this question. I don't know how to answer it.

The question: Show that X $\subset$ $\Re^n$ has measure 0 if and only if ε > 0 there exists an infinite sequence of balls

B_i ={ x $\in$ R^n| |x-a_i | < r_i} with $\sum$ < ε such that X $\subset$ $\cup$_{i=1} ^$\infty$ B_i

 

[micromass]

Such a question belongs in the homework forum: https://www.physicsforums.com/forumdisplay.php?f=152

Also be sure to post an attempt at the solution.