Results 1 to 5 of 5

Math Help - measurable functions

  1. #1
    Newbie
    Joined
    Aug 2010
    Posts
    24

    measurable functions

    Let f be a measurable function and g be a 1-1 function from R to R which has a Lipschitz inverse.

    Show that the composition fog is measurable

    My idea was to take a set (a,00) , then f^-1(a,00) is measurable call this set C , but i need to prove that g^-1(C) is measurable
    Since g^-1 is Lipschitz then it is continuous. Let g^-1 = h , so how can I prove that h(C) is measurable provided that h is Lipschitz, hence continuous ??

    Any ideas please ?? Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member girdav's Avatar
    Joined
    Jul 2009
    From
    Rouen, France
    Posts
    678
    Thanks
    32

    Re: measurable functions

    Can you give information about the set on which f and g are defined?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2010
    Posts
    24

    Re: measurable functions

    It is R the real numbers. I think I mentioned that in the question. Thank you !
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member girdav's Avatar
    Joined
    Jul 2009
    From
    Rouen, France
    Posts
    678
    Thanks
    32

    Re: measurable functions

    Do you mean Borel or Lebesgue measurable?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Aug 2010
    Posts
    24

    Re: measurable functions

    Lebesgue measurable
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Measurable Functions
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: September 27th 2011, 08:50 AM
  2. Measurable functions.
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: April 27th 2011, 09:55 AM
  3. Measurable Functions
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: April 18th 2010, 08:37 AM
  4. measurable functions
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: September 28th 2009, 08:50 AM
  5. measurable functions
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: May 28th 2008, 09:39 PM

Search Tags


/mathhelpforum @mathhelpforum