# Converging almost surely proof

#### oyth94

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

#### Fantini

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.