Convergence of measures#Weak convergence of measures
The Portmanteau theorem is a sentence from the mathematical branch Stochastics and describes equivalent conditions for the weak convergence (also known as convergence in distribution) of random variables. These conditions are in some situations easier than recalculate the definition of weak convergence. The sentence stems from a work by Pavel Sergeyevich Alexandrov from the year 1940.
Wording of the sentence
Be real valued borel - measurable random variables. Then the following statements are equivalent:
Generalizations
The Portmanteau 's theorem can be formulated in general for Polish spaces, apart from the characterization of convergence in distribution on distribution functions.