Can someone explain this notation: $C_w([0,\infty),X)$?

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I am studying a article that appear the notation $$C_w([0,\infty); X)$$ and the explication is that it is the set of weakly-star continuous functions on $[ 0 , \infty)$ with values in $X$ ($X$ is a Banach space). Can somebody explain it? Please. Whats a weakly-star continuous function on $[ 0 , \infty)$ with values in $X$?