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Math Help - Measurable set

  1. #1
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    Measurable set

    Let A\subset\mathbb{R} is measurable set, and let B=\{|x|:x\in A\}. Show that B is also measurable set.

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  2. #2
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    Let C be \{-|x| | x\in A\}. Then it is easy to see that C= \{-x | x \in B\} so if either B or C is measurable, so is the other. But it is also true that A= B\cup C so that if neither B nor C is measurable, then A is not measurable.
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  3. #3
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    But what if A=(\mathbb{Q}\cap [-1,0])\cup ((0,1]-\mathbb{Q}) ? Then B=[0,1], and C=[-1,0], but B\cup C is not equal to A. Sorry if I misunderstood something, od done something wrong.

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