Analytic / CONCEPT

CompactStrassen

For arbitrary real endpoints and Borel probability measures of mass one on their closed interval, equal means and every interval-convex interval-continuous test inequality are equivalent to a single joint probability measure with both exact pushforward marginals and native joint-almost-everywhere conditional expectation of the second coordinate given the first equal to the first. Atomic, singular, and singleton laws are included. Empty-interval support premises are impossible. Coordinate integrability follows from compact marginal support. The construction takes a compact weak limit of finite martingale couplings, preserves both marginals, extends continuous tests to every bounded Borel test, then applies native conditional-expectation uniqueness. The native conditional-expectation identity uses the tested martingale law and integrability on the same joint measure.