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# <math>X_n \ \xrightarrow{\!\!as\!\!}\ X \quad\Rightarrow\quad g(X_n)\ \xrightarrow{\!\!as\!\!}\ g(X).</math>
==Proof==
Spaces ''S'' and ''S′'' are equipped with certain metrics. For simplicity we will denote both of these metrics using the |x−y| notation, even though the metrics may be arbitrary and not necessarily Euclidian.
===Convergence in distribution===
We will need a particular statement from the [[portmanteau theorem]]: that convergence in distribution <math>X_n\xrightarrow{d}X</math> is equivalent to
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