# Almost-sure convergence

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

[Catalogue presentation and source-binding data](https://ocme.evemisslab.com/data/i18n/catalogue.en.json)



## [Almost-sure convergence](https://ocme.evemisslab.com/en/atlas/atlas-almost-sure-convergence/)

Random variables on the same probability space converge almost surely when they converge pointwise outside an exceptional set of probability zero.

atlas-almost-sure-convergence · canonical_mko

[Almost-sure convergence](https://ocme.evemisslab.com/en/mko/mko-almost-sure-convergence/)

## Prerequisite nodes


- [Real random variables on finite sample spaces](https://ocme.evemisslab.com/en/atlas/atlas-random-variable/)
- [Sequence](https://ocme.evemisslab.com/en/atlas/atlas-sequence/)
- [Probability on finite sample spaces](https://ocme.evemisslab.com/en/atlas/atlas-probability/)
- [Sigma-algebras and measure spaces](https://ocme.evemisslab.com/en/atlas/atlas-sigma-algebra-measure-space/)
- [Convergence in probability](https://ocme.evemisslab.com/en/atlas/atlas-convergence-in-probability/)