# Math Help - Measurable Set

1. ## Measurable Set

Hello,

If X and Y are closed sets

Then prove that X + Y is an F-sigma set

Note : X + Y = { k in R^n : k = x + y for x in X and y in Y}

Thanks a ton!

2. Originally Posted by unit1
Hello,

If X and Y are closed sets

Then prove that X + Y is an F-sigma set

Note : X + Y = { k in R^n : k = x + y for x in X and y in Y}

Thanks a ton!
Let { $p_n$} be a dense subset of X (for example a set of points with rational co-ordinates) and { $q_n$} be a dense subset of Y

Then I claim that:

$X + Y = \bigcup_{i=1}^\infty(Y+p_i)\cup(X+q_i)$

3. Hey thanks for that!

I was wondering if it would also work with closed bounded subsets, as in compact subsets?