Support

The support of a function (Def. 5.1.1 ) is the smallest set outside which the function is equal to zero:

$$\text{supp} f= \bar{\{x\in R: f(x) \neq = 0\}}$$

If $$\text{supp}f$$ is bounded (i.e., contained in an interval in the form [a,b] for some $$a,b \in \mathbb{R}$$), then we say that $$f$$ has compact support.