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Math Help - Closed subgroups of R

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    Closed subgroups of R

    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.
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    Quote Originally Posted by Chandru1 View Post
    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 \mathbb{R} as a topological group?
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    yes

    Yes.
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    Quote Originally Posted by Chandru1 View Post
    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.

    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
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