In mathematics, a support set of a real-valued function f defined on a set X, or support set for short, refers to a subset of X that satisfies f that happens to be non-zero on this subset. The most common situation is that X is a topological space, such as a real number axis, etc., and the function f is continuous under this topology. At this time, the supporting set of f is defined as such a closed set C: f is 0 in X\C, and there is no true closed subset of C that also satisfies this condition, that is, C is the smallest of all such subsets One. The support set in the topological sense is the closure of the support set in the sense of the point set. In particular, in probability theory, a probability distribution is the closure of the set of all possible values of a random variable. ( Https://zh.wikipedia.org/wiki/%E6%94%AF%E6%92%91%E9%9B%86 )
The set theory of f supports supp(f)={x∈X|f(x)≠0} is the smallest subset of X, and its complement f is 0. If all points of f(x) except the finite number of points x in X are 0, then f has finite support.
Essential support
ess supp(f)=X\∪{Ω⊂X|Ω is the largest open set, where f is almost everywhere on Ω} is the complement of the largest open set, usually referred to as supp(f)
（https://en.wikipedia.org/wiki/Support_(mathematics)）
In human terms, the support set is a subset of the function, and the function value is not zero in this subset, but the complement of the subset is zero. The number of its elements is the number of non-zero elements.
The support set is the L0 norm