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In case I bugger it up, the union of the support and the kernel of a numerical function make up the domain of that function, correct? Dysprosia 10:12, 17 Jul 2004 (UTC)
Hello I am confused by the statement in "Support": " Singular supports may also be used to understand phenomena special to distribution theory, such as attempts to 'multiply' distributions (squaring the Dirac delta function fails - essentially because the singular supports of two distributions to multiply should be disjoint)." Seems to me if you multiply two distributions whose support is disjoint, you will get zero. Is that not true? Seems to me that the problem in squaring a Dirac Delta has more to do with orders of infinity and limiting processes. Thanks Peter Pdn Feb 20, 2005 4:22 PM EST or 9:22 PM UTC I suppose
But the singular support is not the support. Charles Matthews 22:11, 20 Feb 2005 (UTC)
The "sing supp" is the support w.r.t. the subsheaf C∞ while "supp" is the support w.r.t. the subsheaf {0}. At least some links to sheaf seem necessary to me. MFH 02:14, 12 Mar 2005 (UTC)
Can the concept of support be applied to geometry? I think that would make a good graphical example for newcomers to the idea, if so. The intro is a little hard to parse — Omegatron 20:17, 19 October 2005 (UTC)
Can someone sanity check me on this? The quotes "smallest closed subset F of X such that f = 0 μ-almost everywhere outside F" and "largest open set on which f = 0 μ-almost everywhere" seem unsourced. Are they true? Certainly an arbitrary union of open sets is open (or equivalently the arbitrary intersection of closed sets is closed), but it is not clear to me that an arbitrary union of sets such that f = 0 a.e. will also be a set for which f = 0 a.e.
I checked the citation "Lieb, Elliott; Loss, Michael (2001). Analysis. Graduate Studies in Mathematics. 14 (2nd ed.). American Mathematical Society. p. 13. ISBN 978-0821827833." and they do not characterize it this way, I found it for free here. They define $\Omega^\sim$ to be the set of all open sets such that f = 0 a.e., and then defines the complement of the essential support to be the union over $\Omega^\sim$. But they do not imply that the complement of the essential support is itself in $\Omega^\sim$, while the article here on wiki does make this claim.
I'm suspicious the claim is untrue but even if true it certainly seems unjustified and unsourced. Thoughts?
I clicked this page thinking it was were I could get some SUPPORT for a math question!
While this is clearly a special point, it is more precise to say that the transform qua distribution has singular support {0} [...]
Qua? --Abdull 04:41, 13 June 2006 (UTC)
I don't like this sentence: "In particular, in probability theory, the support of a probability distribution is the closure of the set of possible values of a random variable having that distribution." In probability distribution it is defined better: "The support of a distribution is the smallest closed set whose complement has probability zero." --130.94.162.64 00:57, 21 June 2006 (UTC)
I've taken some analysis, but can't follow this article. It opens
Staying with real-valued functions (e.g., f:R→R) it isn't clear to me if X is a set of real numbers, of real-valued functions, or what. That is, is this saying that the support, S, is defined as
or is it something else? —Ben FrantzDale 13:40, 5 July 2006 (UTC)
In mathematics, the support of a function is, in general, the set of points where the function is not zero. More specifically, a support of a function f from a set X to the real numbers R is a subset Y of X such that f(x) is zero for all x in X that are not in Y.
The "in general" definition is narrower than the "[m]ore specifically" definition! (According to the latter, a function has several supports; according to the former, it has exactly one, which is the smallest possible one according to the latter definition.) Isn't that backwards? --Army1987!! 09:11, 10 July 2008 (UTC)
How about some examples, instead of talking in generalities all the time?
--212.139.126.204 (talk) 14:54, 18 July 2009 (UTC)
I am not sure whether I understood something wrong or if I found a (widespread) mistake. Let us assume:
Can any experienced mathematician correct either me or the article, please? --FDominec (talk) 19:43, 26 October 2009 (UTC)
"In mathematics, the support of a function is the set of points where the function is not zero-valued, or the closure of that set.[1]:678".
In "[1]:678" it states:
Thus the given source doesn't source wp's definition, as "function" and "continuous function" is something different. So either wp's definition has to be changed or another source has to be given. Futhermore "set [...] not zero-valued, or the closure of that set" partly implies that one can choice (maybe based on different definitions) which set it is or that the author/wp doesn't know which set it is. Accourding to the mentioned source it's always the closure of that set (though the closure of that set might be the same as that set).-Yodonothav (talk) 10:37, 26 November 2012 (UTC)
I think this sentence, from the Compact Support section, is problematic:
Functions with compact support in X are those with support that is a compact subset of X. For example, if X is the real line, they are functions of bounded support and therefore vanish at infinity (and negative infinity).
While technically it is true that such functions vanish at infinity, it is a weak statement—they vanish considerably sooner than infinity.
I initially thought that "and therefore [the functions] vanish at infinity" was intended as justification for why functions of bounded support also have compact support. I realized my mistake as soon as I clicked "vanish at infinity" and read the definition. There is no further mention of vanishing at infinity, so I think that it is distracting to bring it up at all. Does anyone else feel the same way? I don't usually edit Wikipedia (except to correct grammar or spelling), so I'm not sure what to do about this. — Preceding unsigned comment added by 137.22.232.216 (talk) 21:58, 17 January 2013 (UTC)
I have changed "and" to "or" in the definition. The definition doesn't seem to make sense with an "and" in it. There can be several meanings of "support", but (within one chosen meaning) "the support" has to be either ... or ... Bj norge (talk) 09:39, 2 July 2013 (UTC)
There seems to be a contradiction between the definition at the top (support "is the set of points where the function is not zero-valued, or the closure of that set" - taking into account the definition of closure) and the later statement that "any superset of a support is also a support". If the term is used with many different meanings then this should be made clear from the beginning in such a way that the article is self-consistent. — Preceding unsigned comment added by 192.76.7.215 (talk) 14:39, 26 September 2013 (UTC)
My immediate reaction to the current intro paragraph is to ask the next classic big ‘W’: why? Why is it all but those that map to zero? What is the purpose?? A good overview intro should answer the questions what, why, where and possibly who and do all those things in simple terms. — Preceding unsigned comment added by 2600:387:6:805:0:0:0:B1 (talk) 15:03, 13 August 2019 (UTC)