What is the function $\mathbb{1}_{[t_i,t_{i+1})}$?

Question

Hello, I am wondering if anyone knows what is meant in the picture above, where it says $\mathbb{1}_{[t_i,t_{i+1})}$. I see it is some sort of function probably dependent on $t_i,t_{i+1}$ but it does not give me a definition of how it depends. I am guessing it takes values $0,1$ depending on $t_i,t_{i+1}$ but don't know the specifics.

I don't see this defined anywhere in the notes. And I tried searching online but the issue is I don't know what it's even called so I can't even start.

Does anyone know? What it's called and how it's defined? Thank you.

The notes is on defining simple stochastic processes by the way.

Answer 1

If $A$ is a set, then $\mathbb{1}_A$ is the indicator function of the set. That is, $\mathbb{1}_A(t) = 1$ if $t \in A$ and $\mathbb{1}_A(t)=0$ if $t \notin A$.

Answer 2

It means characteristic function: a function that takes the value 1 on the indicated set and 0 everywhere else.