supp(f)支撑集

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supp(f)支撑集

2023-09-11 15:35| 来源: 网络整理| 查看: 265

最近看量子的文章中看到一个符号supp(f),之前见过sup(f)问了老板,老板讲解相当于min最小值函数,sub(f)是对一个连续函数f求极小值,(好像是这样,说的不对请指出)。那么supp(f)呢?是一个supp函数还是一个sup函数加上一个p概率?

查了谷歌,在本站看到一位博主写的《函数的支集、支撑集、support、supp》文章https://blog.csdn.net/hqh45/article/details/44593883#commentBox ,知道了supp的符号是support的缩写,是支撑集的意思,但是具体的内容博主只甩了一个谷歌网站,这让没有梯子的兄dei可能望而却步了。那我在这里就做一个搬运工吧。以下是支撑集的维基百科中文释义。

这个我反正没看懂,也没看出和supp有什么关系,然后我去查了support的英文版维基百科的释义。我大体翻译一下。(英语渣)

Formulation:假设f : X\rightarrowR 是一个实值函数,其域(domain)为任意集X。(算了,我还是直接把英文po上吧)

Supppose that f : X\rightarrowR  is a real-valued function whose domain is an arbitrary set X.The set_theoretic support of f,written supp(f), is the set of point in X where f is non-zero \textup{supp}(f)=\left \{ x\in X|f(x)\neq 0 \right \}. The support of f is the smallest subset of X with the property  that f is zero on the subset's complement. If f(x)=0 for all but a finite number of points x in X,then f is said to have finite support.

If the set X has an additional structure (for example, a topology), then the support of f is defined in an analogous way as the smallest subset of X of an appropriate type such that f vanishes in an appropriate sense on its complement. The notion of support also extends in a natural way to functions taking values in more general sets than R and to other objects, such as measures or distributions.

下面就讲了紧支撑(closed support)、奇支撑、支撑族...

 



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