I am currently trying to understand this paper. On page 4 in formula 2 I stumbled upon the letter: $\mathbb{E}$
As I understand it, this typeface is used to represent number sets. I have seen the more common ones (like $\mathbb{N}$) many times before, but have never encountered an E. What set of numbers is represented by the letter $\mathbb{E}$?
On
The notation $\mathbb{E}$ means the expectation of a random variable. Also $\mathbb{P}$ is a probability measure (see https://en.wikipedia.org/wiki/Probability_space). Ins this context $I$ is the indicator function. Let $\Omega$ be a probability space. Recall that if $X:\Omega\longrightarrow\mathbb{R}$ is a random variable it's expectation is defined as:
$$ \mathbb{E}(X):=\int_{\Omega}X(w)d\mathbb{P}(w),$$
where $\mathbb{P}$ is a probability measure (see https://en.wikipedia.org/wiki/Probability_measure). Also, if $A$ is a set, the notation $I$ means:
$$ I_{A}(t)=\begin{cases} 1 & \text{if}\ t\in A, \\ 0 & \text{otherwise.}\end{cases}$$
In particular, you will have:
$$\mathbb{E}(I_{A}(t))=\int_{\Omega}I_{A}(w)d\mathbb{P}(w)=\mathbb{P}(A).$$
It is the expected value of a random variable.