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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 1:37 PM
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On Mar 24, 10:53 am, David C. Ullrich <ullr...@math.okstate.edu>
wrote:
> [. . .]
> 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?

http://groups.google.com/group/sci.math/msg/0cfe35786f2279f0?hl=en

> and such that m(D intersect [0,1]) = 1/2 ?

OK, that's different.

> 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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