Converging almost surely proof

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    Converging Proof
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SUMMARY

The discussion focuses on proving that if a sequence of random variables \(X_n\) converges almost surely to a random variable \(X\), then a function \(f(X_n)\) converges almost surely to \(f(X)\). The participants emphasize the importance of the continuity of the function \(f\) in establishing this convergence. Clarifications regarding the definitions of \(X_n\), \(X\), and the domains and codomains of the function \(f\) are also sought to strengthen the proof.

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  • Familiarity with random variables and their properties
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How do I prove that given Xn converges almost surely to X, that f(Xn) will converge almost surely to f(X)?
 
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Re: converging almost surely proof

Hello oyth! Can you please clarify what is $X_n$, $X$ and what are the domain and codomain of the map $f$? :) Although intuition tells me that probably continuity guarantees what you want, perhaps we can weaken that condition.

Cheers! :D
 

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