Norm of a Function or Square integrable functions

We know that functions can be treated as infinite dimensional vectors . A vector has a norm or length defined for it. How do we do that for a function? Square integrable functions Assume that we have a function: $f: \mathbb{R} \to \mathbb{C}$. It is said to be square integrable if it satisfies the following condition: $$ \int_{-\infty}^{\infty} |f(x)|^2 dx < \infty $$ This is similar to the…