# The Asymptotic Equipartition Property

Introduction :: Convergence :: Data Compression :: Sets

## Introduction

The AEP is the weak law of large numbers as applied to the estimation of entropy.

## The law of large numbers and AEP

The law of large numbers states that for i.i.d. random variables the sum

is close to its expected value

*EX*. (How close? How can we tell?) The AEP states that for i.i.d. r.v.'s,

is close to

*H*(

*X*). To put it another way,