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I am a beginner.

Given probability measure $P$ and sample space $\Omega$, is it true that:

$$\displaystyle \ \ \int_\Omega dP = 1$$

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Looking at your questions so far, I am beginning to find difficult to figure out what are the things you know and those you do not know... For example, the gap betwwen this present question and some others of yours is quite daunting. –  Did Nov 24 '12 at 12:02
    
@did I'm taking a stochastics course with no background in measure theory so I have holes everywhere, unfortunately! –  Jase Nov 24 '12 at 12:16
    
Bad idea. –  Did Nov 24 '12 at 17:19
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1 Answer

up vote 4 down vote accepted

Yes as $$ \int_\Omega \mathrm dP=P(\Omega)=1. $$

More generally $$ \int_A\mathrm dP=\int_\Omega 1_A\,\mathrm dP=P(A),\quad A\in\mathcal{F}. $$

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