Consider an probability space $(\Omega, A,P)$ and the augmented filtration $F(t)= \bigcap_{s>t} \sigma(F^W(t) \cup N),$ where $F^W$ is the natural filtration of an Browian motion $W$ and $N$ the nullsets of $A$.
Why do I need to add in these nullsets in order to make $W$ adapted?
What is the intuition behind this?