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In studying stochastic processes, I have come across the Lebesgue integral applied to a probability space, i.e. $$\int_M f d\textbf{P}$$ But I have also come across the notation $$\int_M f \textbf{P}(d\omega)$$ It seems to me that these are the same, as I have consulted several textbooks which seem to use them at different times in slightly different contexts? Can someone shed some light on this, thanks.

user1008646
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W M Seath
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    Does this answer your question: https://math.stackexchange.com/questions/5230/is-there-any-difference-between-the-notations-int-fxd-mux-and-int-fx? – md5 Jan 28 '20 at 00:35
  • @md5 yes I think it does thank you – W M Seath Jan 28 '20 at 16:53

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