Can someone translate $s_j : \Omega \hspace{3pt} x \hspace{3pt} [0,T_{Final}] \rightarrow S_j \subset R$ into simple English for me?

Can someone translate the following into simplified language? I am familiar with sets and functions, but I am not familiar with such mathematical notation. I have attached a link for more context.

$s_j : \Omega \hspace{3pt} x \hspace{3pt} [0,T_{Final}] \rightarrow S_j \subset R$

- Thank you

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