C Chandru1 Feb 2009 148 10 Chennai Jun 2, 2010 #1 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.

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 Jun 2, 2010 #2 Chandru1 said: 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. Click to expand... Closed in what sense? Closed when considering \(\displaystyle \mathbb{R}\) as a topological group?

Chandru1 said: 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. Click to expand... Closed in what sense? Closed when considering \(\displaystyle \mathbb{R}\) as a topological group?

T tonio Oct 2009 4,261 1,836 Jun 2, 2010 #4 Chandru1 said: 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. Click to expand... Read here A course in p-adic analysis - Google Books . You need exactly the corollary at the top of page 23, and from it it follows at once that the Lebesgue measure of any closed sbgp. is zero. Tonio

Chandru1 said: 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. Click to expand... Read here A course in p-adic analysis - Google Books . You need exactly the corollary at the top of page 23, and from it it follows at once that the Lebesgue measure of any closed sbgp. is zero. Tonio