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.
2026-03-28 03:32:06.1774668726
Notation used in integration in stochastic processes
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