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I am a beginner.

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

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

  • 4
    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](http://math.stackexchange.com/q/243583) is quite daunting.2012-11-24
  • 0
    @did I'm taking a stochastics course with no background in measure theory so I have holes everywhere, unfortunately!2012-11-24
  • 1
    [Bad idea](http://areallybadidea.com/).2012-11-24
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    I like this one because I was planning to write it on some stickers, and make some jokes about the Wau number :D2014-08-07

1 Answers 1

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

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