Talk:Hölder's Inequality for Integrals
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With the full theorem up (and Sequence Space is Lebesgue Space) there is IMHO no need to include the separate statement for sequence spaces. --Lord_Farin 15:02, 11 July 2012 (UTC)
- Okay - feel free to bring this into line with how you think it should be - my own involvement starts when the one-proof wonder Shabab brought this one up at the end of 2009. All I have done since is tidy. --prime mover 19:56, 11 July 2012 (UTC)
Should this be reorganized? There are several statements of versions of the theorem, but one proof not obviously associated with a version. When clicking on some versions, it brings you to a page with no proof. Should we perhaps migrate the proof into the particular version that it is a proof of? Also, the proof for the equality case seems inadequate, as it appears to only handle a single direction. Addem (talk) 15:31, 14 January 2022 (UTC)
- Yeah I would have it so it's:
- Hölder's Inequality
- Hölder's Inequality/Integrals
- Hölder's Inequality for Sums (I know this is technically a subcase of the integral one with the counting measure – but since there are elementary proofs I think it warrants separation)
- Hölder's Inequality
- if that makes sense. A lot of functional analysis needs work. You'll notice that the $L^p$ spaces aren't defined anywhere. Don't be surprised if any page is incomplete or sub-optimal, this area has only really received the attention of a few contributors vs the foundational stuff. Caliburn (talk) 15:43, 14 January 2022 (UTC)
- The above has been done along the broad lines of the above. We still need to extract a version of this which goes back to the original language where simply real numbers are used instead of using the language of measure spaces, Lebesgue spaces and seminorms and so on, because there are many treatments which are accessible to those who have studied Riemann/Darboux integration but not Lebesgue and measure theory. --prime mover (talk) 05:52, 19 May 2023 (UTC)