I saw the following in a journal paper and the notation looks wrong - am I right?
$$t_1 = \sup\{t>0:F(t)>0 \in [0,t]\}$$
I would like to translate this into an English sentence, but I don't understand how $F(t)>0$ can mean $F(t) \in [0,t]$?!
2026-04-08 00:23:06.1775607786
Is $\sup\{t>0:F(t)>0 \in [0,t]\}$ an incorrect math expression?
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I think there are two problems. The first is the last $t$ should probably be a different variable, say $x$. Then the best I can do, and I don't think it says this correctly, is that the range of $t$ for which $F(t) \gt 0$, sometimes called the support of $F$, is a subset (not element) of $[0,x]$. $t_1$ is then the sup of all the $t$'s which have support in $[0,x]$