---
tag: 0A2HNZC44K
kind: concept
name: Convergence in mean
aliases: [convergence-in-lp, lp-convergence, convergence-in-r-th-mean]
msc: [60F25]
sources:
  - url: https://en.wikipedia.org/wiki/Convergence_of_random_variables
    locator: Convergence in mean
---

## Summary

A sequence of random variables converges in $r$-th mean when the expected value of $|X_n - X|^r$ tends to $0$.
The node [[convergence in mean|0TTA57SEJG]] gives the precise definition.