Support

MAS

Suppose that f:X→R is a real-valued function whose domain is an arbitrary set X. The set-theoretic support of f, written $\text{supp}(f)$, is the set of points in X where f is non-zero:

$\text{supp}(f)=x\in X:f(x)\ne 0.$

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.