Meaning of $L^p$, $1\leq p < \infty$

Question

What does "$L^p$, $1\leq p < \infty$" mean? For a finite $p\geq 1$ (e.g. $p=1$ or $p=3$)? Or for all finite $p\geq 1$?

P.S. I understand what $L^p$ means, I just have problems understanding the part about the values of $p$.

Answer 1

This notation typically refers to some $L^p$ space where $p$ is a fixed but unspecified value over the given range, i.e., $p$ is an arbitrary, fixed, finite value greater than or equal to one.