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I have trouble understanding Radon-Nikodym theorem. Here's an example.

Consider the measurable space $(\Omega,F)$, where $\Omega = R$, $F~$ is the $\sigma$-algebra of Borel sets. Let $P[dw] = \frac{1}{\sqrt(2\pi)}e^{-w^2/2}dw$ and $\tilde{P}[dw] = e^{-w}1_{[0,\infty)(w)}dw$ be two probability measures on $\omega$. How to test whether $\tilde{P} << P$ and $P << \tilde{P}$. How do we compute Radon-Nikodym derivative $\frac{d\tilde{P}}{dP}$?

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    Like another question you have asked, this one has no context or motivation. Frankly, it appears to be simply a homework question. What have you tried? What background are you assuming?2010-10-24
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    I got this question from the internet by searching contents on Radon-Nikodym theorem...2010-10-25

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