Show that if M and N are square integrable martingales with continuous paths, then Suppose Wt is a Brownian motion and a ∈ R. Show that the amount of time Brownian motion spends at the point a is...

Show that if M and N are square integrable martingales with continuous paths, then

Suppose W_t
is a Brownian motion and a ∈ R. Show that the amount of time Brownian motion spends at the point a is zero, i.e., that

for all t > 0.