##  [Weak Convergence (of Probability Measures)](/weak-convergence-probability-measures) 

  ##  [Weak Convergence (of Probability Measures)](https://natural.quantumdictionary.io/weak-convergence-probability-measures-0) 

  

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**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A mode of convergence for probability measures on a metric (or topological) space: a sequence of probability measures μ_n converges weakly to μ if ∫ f dμ_n → ∫ f dμ for every bounded continuous test function f (equivalently via distribution functions at continuity points or Portmanteau conditions).