<?xml version="1.0" encoding='utf-8'?>
<!DOCTYPE wml PUBLIC "-//WAPFORUM//DTD WML 1.1//EN" "http://www.wapforum.org/DTD/wml_1.1.xml">
<wml>
<card id="card1" title="Characteristic function (probability theory) - Page 21 - Wikipedia">
<p>
<a accesskey="1" href="page.php?w=Characteristic_function_(probability_theory)&amp;p=20">1.Previous</a><br />
<a accesskey="3" href="page.php?w=Characteristic_function_%28probability_theory%29&amp;p=22">3.Next</a>
</p>
<p>In the univariate case (i.e. when  is scalar-valued) the density function is given by</p>

<p>In the multivariate case it is</p>

<p>where  is the <a href="page.php?w=dot_product">dot product</a>.</p>

<p>The density function is the <a href="page.php?w=Radon-Nikodym_derivative">Radon-Nikodym derivative</a> of the distribution  with respect to the <a href="page.php?w=Lebesgue_measure">Lebesgue measure</a> :</p>

<p><b>Theorem (Lévy)</b>. If  is characteristic function of distribution function , two points  are such that  is a <a href="page.php?w=continuity_set">continuity set</a></p><p>
<a accesskey="1" href="page.php?w=Characteristic_function_(probability_theory)&amp;p=20">1.Previous</a><br />
<a accesskey="3" href="page.php?w=Characteristic_function_%28probability_theory%29&amp;p=22">3.Next</a>
</p>

<do type="prev" label="Search">
        <go href="search.wml"/>
</do>

</card>
</wml>
