Continuous mapping theorem: Difference between revisions

Revision as of 02:27, 13 September 2009

Revision as of 02:29, 13 September 2009

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# <math>X_n \ \xrightarrow{d}\ X \quad\Rightarrow\quad g(X_n)\ \xrightarrow{d}\ g(X);</math>

# <math>X_n \ \xrightarrow{p}\ X \quad\Rightarrow\quad g(X_n)\ \xrightarrow{p}\ g(X);</math>

# <math>X_n \ \xrightarrow{\!\!as\!\!}\ X \quad\Rightarrow\quad g(X_n)\ \xrightarrow{\!\!as\!\!}\ g(X).</math>

==Proof==

===Convergence in distribution===

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===Convergence in probability===

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===Convergence almost surely===

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==References==