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)
Lebesgue Density Theorem
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analysis
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2+5 for a problem copied from a textbook? Really? http://meta.math.stackexchange.com/questions/1803/how-to-ask-a-homework-question – 2011-11-01
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0a problem is a problem!! doesnt matter if its textbook...!! – 2011-11-01
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0As 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 on – 2012-01-25
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0Why 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-real – 2013-04-03