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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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    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}. $