I was studying an article where I encountered $\mathbb{R}^E_{\gt 0}$. I couldn't find out what does this notation mean exactly. I'm sorry if my question is basic, I searched this community but I didn't find the answer to my question.
Here is a part of that article:
Given an undirected graph $G=(V, E)$ with positive edge lengths $l\in\mathbb{R}^E_{\gt 0}$ on which one desires to compute the shortest path from a vertex $s$ to $t$, ...
On
$X^Y$ is the usual notation for the set of functions $Y\to X$. With $X=\mathbb{R}_{>0}$ the positive reals and $Y=E$ the edges, $l\in\mathbb{R}_{>0}^E$ is just a function associating to each edge $e\in E$ a positive real number $l(e)$, its length.
On
The notation $\Bbb R_{>0}^E$ usually means the set of functions from $E$ to $\Bbb R_{>0}$, and $\Bbb R_{>0}:=(0,\infty)$.
However in the cited text it is not so clear what it means. If the edges are numbered then it is possible to interpret $E\subset\Bbb N$, and then $l\in\Bbb R_{>0}^E$ is a function that assign to each $k\in E$ it length $l(k)\in (0,\infty)$.
Where this text comes? Can you give a link to the article?
The short answer: This is just a terse way of saying that the length $l(e)$ of each edge $e$ is a nonnegative real number i.e., $l(e) \in \mathbb{R}_{\ge 0}$. If you are satisfied with this then you can stop reading here.
A longer answer: Note that, in general, a function $f: A \mapsto B$ can be thought of as a vector $f \in B^A$, where for each $a \in A$, the $a$-th coordinate of $f$ is $f(a)$, which is in $B$.
Here $l$ can be thought of as a function $l: E \mapsto \mathbb{R}_{\geq 0}$ and thus a vector in $\mathbb{R}^E_{\ge 0}$, where for each $e \in E$, the $e$-th coordinate of $l$ is $l(e)$, which is in $\mathbb{R}_{\ge 0}$.