I have a question on the following definition in the Forster:

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I don't get the part where it says "Clearly a weak wolution $f$ is a proper, i.e., meromorphic function, solution precisely if $f$ is holomorphic on $X_D$".

First, I don't get why he says "proper i.e. meromorphic", proper and meromorphic functions aren't the same, are they?

Also I would say $f$ is then only a solution on $X_D$ not on the whole of $X$. Why is $f$ then a solution on all of $X$?


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