B_1 measurable w.r.t. F_t t<1

[Bridgeport]

Need to check whether the random variable $B(1)$ is measurable with respect to the sigma-field $F_t=\sigma \{B(s);s\leq t\}$ for any $0\leq t < 1$


$B(t)$ is standard Brownian motion

[Henrylee]

No.

$$ \mathbb{M}\left(B(1)|{\cal F}_t\right)=B(t)\not =B(1) $$