Results 1 to 5 of 5

Math Help - Exercise in Real Analysis

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    3

    Exercise in Real Analysis

    It's the Ex.24 in Chapter 3 Real Analysis (Stein) Does anyone know how to solve it?

    Suppose F is an increasing function on [a,b]
    a). Prove that we can write F= F_A +F_C +F_J
    where F_A is absolutely continuous; F_C is continuous, but F'_C = 0 for a.e. x;
    F_J is a jump function;
    b). Moreover, each component is uniquely determined up to an additive constant.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Bruno J.'s Avatar
    Joined
    Jun 2009
    From
    Canada
    Posts
    1,266
    Thanks
    1
    Awards
    1
    Quote Originally Posted by Gintoki View Post
    It's the Ex.24 in Chapter 3 Real Analysis (Stein) Does anyone know how to solve it?

    Suppose F is an increasing function on [a,b]
    a). Prove that we can write F= F_A +F_C +F_J
    where F_A is absolutely continuous; F_C is continuous, but F'_C = 0 for a.e. x;
    F_J is a jump function;
    b). Moreover, each component is uniquely determined up to an additive constant.
    What does "a.e" mean?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    "A.e." is a technical term meaning "almost everywhere". It means that the property in question holds everywhere except on a set of measure zero.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Bruno J.'s Avatar
    Joined
    Jun 2009
    From
    Canada
    Posts
    1,266
    Thanks
    1
    Awards
    1
    Quote Originally Posted by Ackbeet View Post
    "A.e." is a technical term meaning "almost everywhere". It means that the property in question holds everywhere except on a set of measure zero.
    Well I know what "almost everywhere" means, but I don't know what "for a.e." means. I don't even know what "lol" means.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    "For almost every x"
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. real analysis
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: May 7th 2010, 06:30 AM
  2. real analysis
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: September 12th 2009, 08:29 AM
  3. real analysis
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: September 7th 2009, 05:16 PM
  4. Real Analysis
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: September 3rd 2009, 11:52 AM
  5. real analysis
    Posted in the Calculus Forum
    Replies: 0
    Last Post: January 4th 2007, 08:58 PM

Search Tags


/mathhelpforum @mathhelpforum