##  [Weak Convergence](/weak-convergence) 

  ##  [Weak Convergence](https://natural.quantumdictionary.io/weak-convergence-0) 

  

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**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A sequence of probability measures (μ_n) on a metric space converges weakly to μ if ∫ f dμ_n → ∫ f dμ for every bounded continuous function f; equivalently, distribution functions converge at continuity points of the limit.

 

 

 

 

 





 

 



 ##  [Weak Convergence](https://puremath.quantumdictionary.io/weak-convergence-1) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

Mode of convergence in a topological vector space (typically a Banach or Hilbert space, or space of measures) where a sequence x_n converges weakly to x if every continuous linear functional φ satisfies φ(x_n) → φ(x); in measure spaces this generalizes weak-* or narrow convergence of measures.