I am a beginner.
Given probability measure $P$ and sample space $\Omega$, is it true that:
$$\displaystyle \ \ \int_\Omega dP = 1$$
2026-05-16 18:25:29.1778955929
The Lebesgue integral $\int_\Omega dP$
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Yes as $$ \int_\Omega \mathrm dP=P(\Omega)=1. $$
More generally $$ \int_A\mathrm dP=\int_\Omega 1_A\,\mathrm dP=P(A),\quad A\in\mathcal{F}. $$