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Based on the definition of "proper", it ensures that for inf(sup) problem, the lower/upper bound always exists.
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On the contrary, ERV functions are used for representing constraints, and provide modelling advantages, particularly for stochastic programming (see Rockafellar's 1993 Von Neumann lecture in ''SIAM Review'').
The OR statements preferring restrictions to the effective ___domain are unsourced and erroneous. Using the convexity of the epigraph as the definition avoids the technicalities of bad definitions. <small><span style="border:1px solid black;padding:1px;">[[User:Kiefer.Wolfowitz|<
: I believe I have dealt with these issues by both removing the questionable statements or giving additional sources. [[User:Zfeinst|Zfeinst]] ([[User talk:Zfeinst|talk]]) 22:15, 19 October 2011 (UTC)
== minima of proper convex functions ==
Shouldn't the "properties" section discuss minimization over a convex set? Isn't that often why you care that a function is proper convex (e.g., [[Fenchel duality]])?
I am thinking of statements like those on page 4 of [http://www.myoops.org/cocw/mit/NR/rdonlyres/Electrical-Engineering-and-Computer-Science/6-253Spring2004/8C1E090C-264C-4D2B-AF63-D0953C9CCD98/0/lec_5.pdf]. There are other useful facts later in that handout, e.g., about recession cones. [[User:Eclecticos|Eclecticos]] ([[User talk:Eclecticos|talk]]) 18:54, 2 November 2015 (UTC)
== Domain and effective ___domain ==
The notation for ___domain (<math>\mbox{___domain}(f)</math>) and effective ___domain (<math>\mbox{dom}(f)</math>) can be easily confused by a novice. Whenever possible I explicitly use <math>X</math> instead of ___domain. <!-- Template:Unsigned --><small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:David Pal|David Pal]] ([[User talk:David Pal#top|talk]] • [[Special:Contributions/David Pal|contribs]]) 22:59, 8 December 2023 (UTC)</small> <!--Autosigned by SineBot-->
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