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# Introduction
![[Pasted image 20250509115117.png]]
# Modes de convergence
## Convergence presque sûre
![[Pasted image 20250509115312.png]]
![[Pasted image 20250509115427.png]]
![[Pasted image 20250509115532.png]]
## Convergence en $L^{2}$
![[Pasted image 20250509115732.png]]
![[Pasted image 20250509115752.png]]
## Convergence en probabilité
![[Pasted image 20250509115818.png]]
![[Pasted image 20250509115844.png]]
## Convergence en loi
![[Pasted image 20250509115929.png]]
![[Pasted image 20250509120047.png]]
![[Pasted image 20250509120156.png]]
# Théorèmes de convergence
## Loi faible des grands nombres (CV en probabilité)
![[Pasted image 20250509120611.png]]
## Loi forte des grands nombres (CV presque sûre)
![[Pasted image 20250509120700.png]]
## Théorème central limite (CV en loi + loi)
![[Pasted image 20250509120902.png]]
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