Convergence in distribution

2020 Mathematics Subject Classification: Primary: 60B10 [MSN][ZBL]

Convergence of a sequence of random variables  defined on a certain probability space , to a random variable , defined in the following way:  if

| (*)

|

for any bounded continuous function . This form of convergence is so called because condition (*) is equivalent to the convergence of the distribution functions  to the distribution function  at every point  at which  is continuous.

#### Comments[edit]

See also Convergence, types of; Distributions, convergence of.

This is special terminology for real-valued random variables for what is generally known as weak convergence of probability measures (same definition as in (*), but with ,  taking values in possibly more general spaces).