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# quick q on norms watch

1. if i want to prove that the formula ||f||_1 = integral of |f| between 0 and 1 defines a norm on the vector space C[0,1] of cts functions f:[0,1]->R then this means i want to prove the properties:
integral of |f| between 0 and 1 >= 0, integral of |f| between 0 and 1 = 0 <=> f = 0
and
for all y in R integral of |yf| between 0 and 1 = y * integral of |f| between 0 and 1
etc.

just want to check the form im using 'as my norm' is actually correct?
2. You also want to prove the triangle inequality, i.e.

Your other two criteria are correct (although you may want to use the letter "c" rather than "y" to denote a constant real number for your second condition)
3. heh yeah i couldnt be bothered to write that bit hence the etc. you've answered my question though, thanks!

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Updated: November 9, 2008
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