Closed subgroups of R

Feb 2009
148
10
Chennai
Find all the closed subgroups of (R,+)? And if H is any proper subgroup of (R,+) then prove that m(H)=0, where m = lebesgue measure.
 

Drexel28

MHF Hall of Honor
Nov 2009
4,563
1,566
Berkeley, California
Find all the closed subgroups of (R,+)? And if H is any proper subgroup of (R,+) then prove that m(H)=0, where m = lebesgue measure.
Closed in what sense? Closed when considering \(\displaystyle \mathbb{R}\) as a topological group?