Converging almost surely proof

oyth94 · Jul 24, 2013

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 · Jul 24, 2013

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

Converging almost surely proof

Discussion

Graduate Probability puzzle

Undergrad The problem of points

Undergrad The countability paradox of computable numbers

Undergrad How does axiom of foundation prevent infinite sequence of elements?

Undergrad I don't understand Dedekind cuts

Graduate Cannot understand this corollary on surreal numbers

High School Bunkbed Conjecture Debunked?

Insights Revisiting the Velocity-Time Function

Insights Remote Operated Gate Control System

Insights AI Enriched Problem Solving

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

Converging almost surely proof

Discussion

Similar threads

Graduate Convergence in measure vs Almost surely convergence

Graduate Two independent random vectors are almost surely non-orthogonal

Graduate Understanding the Concept of Almost Surely in Probability

Graduate Almost sure convergance of sum of rv

Graduate Does bounded almost surely imply bounded in Lp?

Graduate Does (X_{n})_{n_{\geq 1}} converge almost surely to 0?

Graduate How can we prove that E(X)=0 if X=0 almost surely?

Graduate Does E(e^{-X}) = 0 imply X = \infty almost surely for X \geq 0?

TFAE proof involving limit and convergent sequence

Graduate Convergence in Measure: Understanding and Proving Almost Everywhere Convergence