Convergence in distribution
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.
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).
Convergence in distribution. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Convergence_in_distribution&oldid=20859