Converging almost surely proof

[oyth94]

How do I prove that given X_n converges almost surely to X, that f(X_n) will converge almost surely to f(X)?

 

[Fantini]

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!