Convergence in probability
From Encyclopedia of Mathematics
2020 Mathematics Subject Classification: Primary: 60-01 Secondary: 28A20 [MSN][ZBL]
Convergence of a sequence of random variables 
defined on a probability space 
, to a random variable 
, defined in the following way: 
if for any 
,
 |
In mathematical analysis, this form of convergence is called convergence in measure. Convergence in distribution follows from convergence in probability.
Comments
See also Weak convergence of probability measures; Convergence, types of; Distributions, convergence of.
How to Cite This Entry:
Convergence in probability. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Convergence_in_probability&oldid=20866
Convergence in probability. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Convergence_in_probability&oldid=20866
This article was adapted from an original article by V.I. Bityutskov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article