Skorohod discovered that if a sequence
Q
n
{Q_n}
of countably additive probabilities on a Polish space converges in the weak star topology, then, on a standard probability space, there are
Q
n
{Q_n}
-distributed
f
n
{f_n}
which converge almost surely. This note strengthens Skorohod’s result by associating, with each probability
Q
Q
on a Polish space, a random variable
f
Q
{f_Q}
on a fixed standard probability space so that for each
Q
Q
, (a)
f
Q
{f_Q}
has distribution
Q
Q
and (b) with probability 1,
f
P
{f_P}
is continuous at
P
=
Q
P = Q
.