Talk:Function is Convex iff Epigraph is Convex

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This article, or a section of it, needs explaining. In particular: Sorry, what is the definition of convexity here? I added a definition using epigraph. Probably Definition:Convex Real Function/Definition 1 must be extended to $\R^n$-case. I don't expletive know, I just copied this expletive definition from the expletive dictionary. The current Definition:Convex Real-Valued Function may be replaced by the one from your dictionary, or we add it as a second definition and this theorem could be renamed to 'Definition Equivalences'. Where's your source? This remains as an equivalence proof. We've had too many cases where clever contributors enter definitions out of their own cleverness which end up being incorrect. Hence we are wary about trusting unsourced definitions. My source is 'Rockafellar', as given in Definition:Convex Real-Valued Function/Real Vector Space. We need several definitions for convexity. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Explain}} from the code.

The validity of the material on this page is questionable. In particular: You need to specify the domain of $f$. Definition:Real-Valued Function is too general, in particular, the domain is not a vector space. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by resolving the issues. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Questionable}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Well volunteered. Thank you for calling this thin spot to our attention.

If you have the background to understand it this well enough, you may be able to plant the foundations as deeply as you may, as long as there is an immediately accessible route in through the mind.

The image of a convex real function is such that all its points are above the line is an essential mental image for the early student.

Monday morning latest, please. :-) --prime mover (talk) 20:16, 17 October 2023 (UTC)