Talk:Indicator function (convex analysis)
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Shouldn't one also adopt the convention $0\cdot \infty=0$?92.227.15.192 (talk) 16:13, 22 April 2015 (UTC)
In all books of convex analysis this function (taking values $0$ and $\infty$) is called indicator function. 91.32.18.76 (talk) 18:26, 14 October 2015 (UTC)
Rockafellar 1970 book calls this function the indicator function as do all standard convex analysis books. The characteristic function used in integration is the one taking values 0 or 1. — Preceding unsigned comment added by 206.87.39.202 (talk) 18:37, 26 April 2017 (UTC)
And clearly, this function is not convex (unless the given set is convex). Boris Tsirelson (talk) 16:31, 19 December 2018 (UTC)
Characteristic versus indicator
[edit]This article is just confusing. The function in this article is called indicator function in all books on convex analysis, in particular in the cited book by Rockafellar (page 28 of the 1997 edition). (Convex) analysis and probability theory simply use different terminology and this is mixed up in this article ("usual indicator function"). 147.188.251.8 (talk) 21:46, 11 February 2024 (UTC)
- I agree with you, those of Rockafellar, JBHU, Boyd and Bauschke/Combettes for example all do that (if this is not enough...).
- I think it should be accepted that each field has its "indicator" and "characteristic" functions :
- - in probabilities, they usually call "indicator function" the one with range {0,1} (even on the corresponding wikipedia page), and the characteristic function has a totally different meaning linked to Fourier transforms (see once again the corresponding wikipedia page),
- - in complex analysis the "indicator function" is totally different (see for yourself).
- I'll change the title since everybody seems to agree with that opinion (otherwise a good reason needs to be provided, and at least a set of references that matches the above cited).
- I don't think that the original authors were much into the field of convex analysis, the last part concerning the subdifferential was wrong. Trashyyy (talk) 10:48, 2 September 2025 (UTC)