Results 1 to 2 of 2

Math Help - limsup and liminf

  1. #1
    Newbie
    Joined
    Oct 2012
    From
    Seoul
    Posts
    16

    limsup and liminf

    I have a question on the definition of limsup and liminf.

    First let A_k =  [a_n | n \geq k} with  A_k \subset A_{k-1} \subset ... \subset A_1

    s_n = SupA_n, l_n = Inf A_n

     s_1 \geq s_2 ... \geq s_n,  l_1 \leq l_2 ... \leq l_n

     limsup a_n = lim_{k -> \infty} Sup A

     liminf a_n= lim_{k -> \infty} Inf A

    I don't understand  s_1 \geq s_2 ... \geq s_n, l_1 \leq l_2 ... \leq l_n

    Why is   l_1 \leq l_2 ... \leq l_n
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,616
    Thanks
    1579
    Awards
    1

    Re: limsup and liminf

    Quote Originally Posted by rokman54 View Post
    Why is   l_1 \leq l_2 ... \leq l_n

    For bounded sets C~\&~D if C\subset D then surely you understand that
    \sup(D)\ge\sup(C)~\&~\inf(D)\le\inf(C)~?

    In this case A_n\subset A_1 so l_1\le l_n.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. prove limsup-liminf<2
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: December 6th 2011, 03:15 PM
  2. [SOLVED] limsup and liminf
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: September 21st 2010, 05:09 AM
  3. Liminf to limsup
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: November 20th 2009, 10:49 AM
  4. A problem with limsup/liminf
    Posted in the Calculus Forum
    Replies: 4
    Last Post: January 8th 2009, 01:20 PM
  5. limsup and liminf
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 29th 2007, 09:05 AM

Search Tags


/mathhelpforum @mathhelpforum