  In this paper, a quantitative estimate of unique continuation for the
stochastic heat equation with bounded potentials on the whole Euclidean space
is established. This paper generalizes the earlier results in [29] and [17]
from a bounded domain to an unbounded one. The proof is based on the locally
parabolic-type frequency function method. An observability estimate from
measurable sets in time for the same equation is also derived.
