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m →Convergence almost surely: improve html maths |
m →Convergence almost surely: improve html maths |
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===Convergence almost surely===
By definition of the continuity of the function ''g''(·),
: <math>
\lim_{n\to\infty}X_n(\omega) = X(\omega) \quad\Rightarrow\quad \lim_{n\to\infty}g(X_n(\omega)) = g(X(\omega))
</math>
at each point ''X''(''ω
: <math>\begin{align}
\operatorname{Pr}\Big(\lim_{n\to\infty}g(X_n) = g(X)\Big)
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