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

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David C. Ullrich

Posts: 21,553
Registered: 12/6/04
Re: Half Measure and Correction
Posted: Mar 24, 2013 2:49 PM
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On Sun, 24 Mar 2013 10:37:46 -0700 (PDT), Butch Malahide
<fred.galvin@gmail.com> wrote:

>On Mar 24, 10:53 am, David C. Ullrich <ullr...@math.okstate.edu>

>> [. . .]
>> So the more interesting version of the question,
>> in any case less trivial, amounts to this: Is there
>> a measurable set D such that
>>   0 < m(D intersect I) < m(I)
>> for every open interval I,

>Didn't we just have that thread?



>> and such that m(D intersect [0,1]) = 1/2 ?
>OK, that's different.

Precisely! heh.

>> The answer is yes, by the way. Think about
>> "fat Cantor sets". Start with a Cantor set, then
>> add some more Cantor sets, one in each interval
>> the first set misses. Repeat until done...

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