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Problem from Folland : based on Lebesgue Density Theorem: Let $D_{E}(x) = \lim_{r\to 0}\frac{\mu(E\cap B(r,x))}{\mu(B(r,x))}$ whenever it exists. Find examples of $E$ and $x$ such that $D_{E}(x)$ is a given number $\alpha \in (0,1)$ , or such that $D_{E}(x)$ does not exist. ($X = \mathbb{R}^n$,$\mu$ is Lebesgue measure)

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    +5 for a problem copied from a textbook? Really? http://meta.math.stackexchange.com/questions/1803/how-to-ask-a-homework-question2011-11-01
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    a problem is a problem!! doesnt matter if its textbook...!!2011-11-01
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    As Nate is probably implying or suggesting, you need to show more indications of where you are stuck, which parts of the question you do or don't understand, and so on2012-01-25
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    Why does this question has 6 negative votes? There are a lot of questions more stupid with a lot more positive votes... http://math.stackexchange.com/questions/54506/is-this-batman-equation-for-real2013-04-03

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