User talk:Caliburn/s/mt/LpStuff

You will have notice some small changes I already made. Some further recommendations based on reading:


 * Definition:Almost All does not link directly to the measure-theoretic concept. Recommend a specific redirect to Definition:Almost Everywhere.
 * To me, Definition:Equality Almost Everywhere has a more natural ring to it than Definition:Almost-Everywhere Equality.
 * It would be natural to have Definition:Equality Almost Everywhere and Definition:Almost-Everywhere Equality Relation on the same page, probably the latter transcluded onto the former.
 * On User:Caliburn/s/mt/Definition:Lp Space/Vector Space you introduce the notation for $\MM$ but define for $L^p$
 * To keep User:Caliburn/s/mt/Definition:Lp Space structured and intelligible, we probably need to restrict what is transcluded on there. I would suggest just vector space, normed vector space, and $L^\infty$, leaving the definition of the norm itself as a separate one.
 * There is/remains some unclarity as to whether measurable functions are real-valued $\R$ or extended real-valued $\overline\R$. This works on towards these higher-level definitions. How do you suggest we deal with this?
 * For readability's sake, it is the most elegant when all page links use rendered versions of "Lp", i.e. $L^p$ Norm is Norm, similar with $p$-seminorm etc.

Thanks for your efforts putting this on a solid footing. Please understand the recommendations as my suggestions to possibly improve the result, not to criticise anything.

With the above amendments taken into account, I would say that the material is ready to leave user-space. Nice work! &mdash; Lord_Farin (talk) 12:17, 22 May 2022 (UTC)


 * I'll change all those links to almost everywhere. Equality Almost Everywhere sounds better for me too. I should mention that I'm restricting $+$ and $\cdot$ to $L^p$. Fine with restructuring the $L^p$ spaces page like that. As to whether I want to use $\overline \R$ or $\R$, obviously $\overline \R$ is a bit more finicky because addition is not always defined. I might change it all to $\R$ for now and then look at what can be changed to $\overline \R$ later. Last point will do. It's not quite ready to leave userspace yet, there's still some redlinks that need to be filled in, though if you have work to do that depends on this I can make it the next thing I get to. I got distracted with FA. Thanks for the feedback! Caliburn (talk) 13:44, 22 May 2022 (UTC)