Continuous mapping theorem: Difference between revisions

Revision as of 19:37, 26 June 2019

Revision as of 17:56, 16 October 2019

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\begin{align}

X_n \ \xrightarrow\text{d}\ X \quad & \Rightarrow\quad g(X_n)\ \xrightarrowxleftarrow\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).