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I' am reading about the zero set of Brownian motion from Introduction to Stochastic Processes by Lawler.

Let $X_t$ be a Brownian motion and define the following random set:

$Z=\{t:X_t=0\}$

Lawler then goes on to discuss the topological properties of this set $Z$. I'll quote from the book:

One topological property the $Z$ satisfies is the fact that $Z$ is a closed set. This means that if a sequence of points $t_i\in Z$ and $t_i\to t$, then $t\in Z$. This follows from the continuity of the function $X_t$. For continuous function, if $t_i\to t$, then $X_t\to X$.

What does the $\to$ symbol mean?

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    $\begingroup$ it means 'converges to' $\endgroup$ – user83346 Dec 22 '15 at 14:57
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The symbol $\to$ means "converges to", that is $t_i\to t$ means $\lim_{i\to +\infty}t_i=t$.

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