Homework Help: Show that X ⊂ ℜn has measure 0 if and only if ε > 0

1. Dec 3, 2011

Riam

1. The problem statement, all variables and given/known data

The question: Show that X ⊂ ℜn has measure 0 if and only if ε > 0 there exists an infinite sequence of balls

B_i ={ x ∈ R^n| |x-a_i | < r_i} with ∑ r$^{n}_{i}$ < ε such that X ⊂ ∪ $^{\infty}_{i =1}$B_i

2. Relevant equations

3. The attempt at a solution

2. Dec 3, 2011

gb7nash

Re: measures

What have you tried?

3. Dec 3, 2011

micromass

Re: measures

Please post an attempt at the solution or this thread will be deleted.

Also it might be necessary to define your terms. How did you define "measure 0" etc.

4. Dec 3, 2011

Riam

Re: measures

I said
choose ε > 0, , for n = 1, i = 1, let a be the center of the ball and raduis r. if | x- a| < r with Ʃ r < ε such that X $\subset$ B$_{1}$. and keep trying for n =2 and generalise it? this is my guess?

5. Dec 3, 2011

micromass

Re: measures

And how did you define "measure 0"??