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Formula/definition in 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.

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2 Answers 2

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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 $t \notin A$.

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  • $\begingroup$ Ah, that makes it clearer, thank you! $\endgroup$
    – Melba1993
    Nov 30, 2015 at 0:12
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It means characteristic function: a function that takes the value 1 on the indicated set and 0 everywhere else.

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  • $\begingroup$ In probability theory (as in the reference shown) the term characteristic function means something else. $\endgroup$
    – GEdgar
    Nov 29, 2015 at 23:51
  • $\begingroup$ I will buy indicator, no problem. $\endgroup$
    – Justpassingby
    Nov 29, 2015 at 23:52

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