Continuous mapping theorem: Difference between revisions

Revision as of 19:03, 30 March 2019

Revision as of 19:04, 30 March 2019

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X_n \ \xrightarrow\text{d}\ X \quad & \Rightarrow\quad g(X_n)\ \xrightarrow\text{d}\ g(X); \\[6pt]

X_n \ \xrightarrow\text{p}\ X \quad & \Rightarrow\quad g(X_n)\ \xrightarrow\text{p}\ g(X); \\[6pt]

X_n \ \xrightarrow{\!\!\text{a.s.}\!\!}\ X \quad & \Rightarrow\quad g(X_n)\ \xrightarrow{\!\!\text{a.s.}\!\!}\ g(X).

\end{align}

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