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Possible Duplicate:
Understanding denseness of $C^\infty$ in $L^p$ space.

I am looking for a proof that shows $C^\infty(\Omega)$ is dense in $L^p(\Omega)$ . Any hints would be appreciated. Where $\Omega\subset \mathbb R^n$.

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    What is $\Omega$?2012-05-20
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    Its a bounded, open connected subset of $\mathbb R^n$2012-05-20
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    1. Show the continuous functions with compact support are dense. 2. Use [mollifiers](http://en.wikipedia.org/wiki/Mollifier) to approximate continuous functions uniformly by smooth functions.2012-05-20
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    @t.b. can you explain me why do we have to take continuous functions to have compact support ?2012-05-20
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    @Ananda I would think that's because otherwise you're not sure whether the convolution exists. But if $f,g$ both have compact support then $f \ast g$ exists. See [here](http://en.wikipedia.org/wiki/Convolution#Compactly_supported_functions).2012-05-20
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    [This](http://math.stackexchange.com/questions/67370/smooth-functions-with-compact-support-are-dense-in-l1) is related.2012-05-20
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    Aren't polynomials dense in $L^p(\Omega)$?2012-05-20
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    Ok, I missed that your $\Omega$ is open. But again, [this](http://www.math.ucsd.edu/~bdriver/240A-C-03-04/Lecture_Notes/Older-Versions/chap22.pdf) might be helpful ;-)2012-05-20

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