In mathematics and statistics, Skorokhod's representation theorem is a result that shows that a weakly convergent sequence of probability measures whose limit measure is sufficiently well-behaved can be represented as the distribution/law of a pointwise convergent sequence of random variables defined on a common probability space.
It is named for the Ukrainian mathematician A. V. Skorokhod.
μ
be a sequence of probability measures on a metric space
μ
converges weakly to some probability measure
μ
Suppose also that the support of
μ
-valued random variables
defined on a common probability space
such that the law of
μ