In the following lecture given by Fredric Schuller, he mentions this during the lecture which is on multilinear algebra (know that $P$ is a set of polynomials such that $p$ $\in$ $P$):
“consider the map $I$: $P$ $\to$ $\mathbb{R}$, now I need to say how a polynomial is mapped to a real number
$I(p)$ $:= $$\int_0^1$$p(x)dx$“
My questions is: What does he mean when he says “how a polynomial is mapped to a real number”? Is he simply referring to the definition of $I$? I’ve just never heard someone say that instead of saying “The map $I$ is defined as...”
He is just defining the mapping. He is saying: I am defining a mapping $I: P \to \mathbb{R}$ which assigns to each polynomial $p(x)$ the real number $\int_0^1 p(x) dx$.