Results 1 to 4 of 4

Math Help - lebesgue measurable sets

  1. #1
    Newbie
    Joined
    Jul 2007
    Posts
    13

    lebesgue measurable sets

    Let' A be a subset of R such that between two its members there is a point that does not belong to A.Is A surly lebesgue measurable?If it is ,can we say it's lebesgue measure is zero.Or it is nothing to say about A.Please guide me.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,939
    Thanks
    338
    Awards
    1
    Quote Originally Posted by mazaheri View Post
    Let' A be a subset of R such that between two its members there is a point that does not belong to A.Is A surly lebesgue measurable?If it is ,can we say it's lebesgue measure is zero.Or it is nothing to say about A.Please guide me.
    I'm not an expert, but see this link. In particular look at property 3. My question to you would be that if you don't know if A can be measured, can you measure its compliment? If you can do so, then you can measure A as well.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member Rebesques's Avatar
    Joined
    Jul 2005
    From
    At my house.
    Posts
    538
    Thanks
    11
    I think the Cantor set answers your question.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by mazaheri View Post
    Let A be a subset of R such that between two its members there is a point that does not belong to A.Is A surly lebesgue measurable?If it is ,can we say it's lebesgue measure is zero.Or it is nothing to say about A.Please guide me.
    The set of irrational numbers satisfies the hypothesis, but its measure is not zero.

    In fact, from the given hypothesis you cannot even conclude that A is measurable. Let B be any non-measurable subset of R and let A be the set of irrational numbers in B. Then A is also non-measurable, and between any two elements of A there is a rational number that is not in A.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. E-E for a Lebesgue measurable set E contains some box?
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: November 21st 2011, 02:26 PM
  2. Non-Lebesgue Measurable
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 4th 2010, 04:11 PM
  3. is R Lebesgue-measurable?
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: May 30th 2010, 01:46 AM
  4. lebesgue measurable set
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: January 11th 2010, 12:01 AM
  5. lebesgue measurable function
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: November 22nd 2009, 08:11 AM

Search Tags


/mathhelpforum @mathhelpforum