# What is this mathematics sub-field called?

I would love to answer another question on this site, but I am totally unfamiliar with the required technique. I mean, I don't even know the sub-field's name.

The field I am looking for is one that is concerned with the optimisation of (probability or cumulative density) functions w.r.t. some integral.

What is the appropriate (nearest) field?

• – Rahul Nov 8 '13 at 17:09
• @RahulNarain Thank you. Would you say that the Cantor function, the Devil's staircase, which is mentioned in the cont. game theory wiki, is something one might get to by using CoV techniques? – Keep these mind Nov 8 '13 at 17:34
• It reminds me an example of a game without a value. I tried to show its upper value is strictly larger than lower value, and faces the same problem.en.wikipedia.org/wiki/Example_of_a_game_without_a_value There might be some clue in the cited paper by Sion and Wolfe, which I have no access to. – Metta World Peace Nov 8 '13 at 17:55

• Thanks. 1) I was hoping that the restriction that the sought functions must be probability density functions might yield a more simple analysis. And 2) I think (but I'm quite unsure) that my problem doesn't require smoothness, whereas CoV does? I.e., the space of all pdfs/cdfs on $[0,1]$ doesn't seem appropriate for CoV. Am I wrong? Any further guidance? – Keep these mind Nov 8 '13 at 17:26