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Math Help - proving a set is measurable

  1. #1
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    proving a set is measurable

    Question:
    Suppose that A is a subset of \mathbb{R} with the property that for every
    \epsilon > 0 there are measurable sets B and C such that B \subset A
    \subset C and m(C \cap B^c) < \epsilon. Prove that A is measurable.

    My attempt:
    Im finding this stuff really tricky! I know the definition of a set
    being measurable but having real difficulty showing it. I know that i have
    to use the fact that B and C are both measurable, but dont know what set to
    use in the definition! help please! thanks
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  2. #2
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    Quote Originally Posted by ramdayal9 View Post
    Question:
    Suppose that A is a subset of \mathbb{R} with the property that for every
    \epsilon > 0 there are measurable sets B and C such that B \subset A
    \subset C and m(C \cap B^c) < \epsilon. Prove that A is measurable.

    My attempt:
    Im finding this stuff really tricky! I know the definition of a set
    being measurable but having real difficulty showing it. I know that i have
    to use the fact that B and C are both measurable, but dont know what set to
    use in the definition! help please! thanks

    Ok, what is the definition of "measurable set" that you have?

    Tonio
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  3. #3
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    A set K is measurable if for all E \subset R, m(E) = m(K \cap E) + m(K^c \cap E)
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  4. #4
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    Quote Originally Posted by ramdayal9 View Post
    A set K is measurable if for all E \subset R, m(E) = m(K \cap E) + m(K^c \cap E)

    This must be the OP I pressume: E \subset R, m(E) = m(K \cap E) + m(K^c \cap E)
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  5. #5
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    Quote Originally Posted by ramdayal9 View Post
    Question:
    Suppose that A is a subset of \mathbb{R} with the property that for every
    \epsilon > 0 there are measurable sets B and C such that B \subset A<br />
\subset C \,\,and \,\,m(C \cap B^c) < \epsilon. Prove that A is measurable.

    My attempt:
    Im finding this stuff really tricky! I know the definition of a set
    being measurable but having real difficulty showing it. I know that i have
    to use the fact that B and C are both measurable, but dont know what set to
    use in the definition! help please! thanks
    .
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