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

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quasi

Posts: 10,188
Registered: 7/15/05
Re: Half Measure and Correction
Posted: Mar 24, 2013 2:35 AM
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Butch Malahide wrote:
>quasi 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.


Yes, that's what I meant.

quasi



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