  For a continuous ${\cal L}_2$-bounded Martingale with no intervals of
constancy, starting at $0$ and having final variance $\sigma^2$, the expected
local time at $x \in \cal{R}$ is at most $\sqrt{\sigma^2+x^2}-|x|$. This sharp
bound is attained by Standard Brownian Motion stopped at the first exit time
from the interval $(x-\sqrt{\sigma^2+x^2},x+\sqrt{\sigma^2+x^2})$. Sharp bounds
for the expected maximum, maximal absolute value, maximal diameter and maximal
number of upcrossings of intervals, have been established by Dubins and Schwarz
(1988), Dubins, Gilat and Meilijson (2009) and by the authors (2017).
