View source for Convergence in probability

Convergence of a sequence of random variables <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026080/c0260801.png" /> defined on a probability space <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026080/c0260802.png" />, to a random variable <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026080/c0260803.png" />, defined in the following way: <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026080/c0260804.png" /> if for any <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026080/c0260805.png" />,

<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026080/c0260806.png" /></td> </tr></table>

In mathematical analysis, this form of convergence is called convergence in measure. [[Convergence in distribution|Convergence in distribution]] follows from convergence in probability.



====Comments====
See also [[Weak convergence of probability measures|Weak convergence of probability measures]]; [[Convergence, types of|Convergence, types of]]; [[Distributions, convergence of|Distributions, convergence of]].