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http://www.scribd.com/doc/90975254/Attempt-Explanation-Szhwarz-Space

questions is in link. I tried to upload it on the site but I did not manage to upload images. Sorry.

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    Why don't you consider typing it up?2012-04-24

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The second question is clearly (?) a misprint: the word "space" is missing. A semi-norm is something weaker than a norm. As you understood, $p(x)=0$ does not imply that $x=0$, if $p$ is only a semi-norm. Look here for a definition.