Talk:Minkowski inequality

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[edit] proof is incomplete

The proof is incomplete as one of the conditions to use Hoelder's inequality is in this case that |f+g|^{p-1} \in L^q or equivalently that |f+g| \in L^p. To avoid reasoning circularly this would have to be proved without using the Minkowski inequality. Anybody knows how to do this in a nice way? --MarSch 13:58, 1 October 2007 (UTC)

This condition is not necessary for the use of Holder's inequality (it is only used if one wants to prove that both sides of Holder's inequality are finite). R.e.b. 15:20, 1 October 2007 (UTC)
The current proof of Hölder's inequality uses this finiteness condition to justify, in effect, division (normalization). So if what you say is correct then the problem has merely shifted from here to there. --MarSch 13:23, 2 October 2007 (UTC)
Holder's inequality holds trivially if one of the functions has infinite norm. R.e.b. 14:59, 2 October 2007 (UTC)

You are correct of course. --MarSch 16:58, 2 October 2007 (UTC)

The division by (\|f + g\|_p)^{p-1} at the end of the proof also requires that finiteness of \|f + g\|_p has been proven. --MarSch 10:54, 3 October 2007 (UTC)

Okay, I think we're all good now. Thanks R.e.b.. --MarSch 12:19, 4 October 2007 (UTC)