Function Notation with "|"

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What does that following notation mean in english?

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In this case, J is a set, but I am not sure how the "|" relates the set to the function f.

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It means that the domain of the function, say the domain is the set $D$, is restricted to an smaller set $J \subset D$

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"$f|_J$" means "$f$ restricted to $J$".