Date: Mar 24, 2013 2:35 AM
Author: quasi
Subject: Re: Half Measure and Correction

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