I am reading up on this concept. My teacher says not to worry about the set of all borel measures P(x) that the prokhorov metric is usually defined on,nor the borel sigma field and just focus on figuring out convergence of a sequence of measures in any general metric space. To my undertsnding there doesnt seem to be an easy way to describe this without mentioning borel sigma fields. he said to just take a set S consisting of a bunch of measures and describe how we would extend conventional metric space convergence of sequences to this. Since the set S is a collction of measures can we define the prokhorov metric on it and make it into a metric space?