Strange right-arrow symbol ([itex]\mapsto[/itex]) in stochastic calculus.

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What does the right arrow mean in this context:

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...Then the process [itex]t \mapsto \int_{0}^t \phi_s dM_s[/itex] are well-defined continuous local martingales, whose quadratic variations are given by ...

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Is this supposed to mean "the process [itex]X[/itex] that is the mapping [itex]X: t \mapsto \int_{0}^t \phi_s dM_s[/itex]"
 
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Yes, that indicates a "mapping". t is mapped to [itex]\int_0^t \phi_s dM_s[/itex].