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Topic: Half Measure
Replies: 14   Last Post: Mar 25, 2013 5:03 PM

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Butch Malahide

Posts: 894
Registered: 6/29/05
Re: Half Measure and Correction
Posted: Mar 24, 2013 1:01 AM
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On Mar 23, 11:01 pm, quasi <qu...@null.set> wrote:
> William Elliot wrote:
> >Question:  Is there a dense D, subset of R with
> >empty interior and measure D /\ [0,1] = 1/2?

>
> Yes.
>
> Let
>
>    A = (0,1/2)\Q
>
>    B = Q\A
>
>    D = A U B


Then B = Q\A = Q, and D = A U Q = (0,1/2) U Q has nonempty interior.

Of course you meant to say B = Q\(0,1/2), so that A is the symmetric
difference of (0,1/2) and Q.




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