A proof that every nonvoid "weak" closed convex set of distributions on the unit interval is the set of all optimal strategies for one player in some game with continuous payoff over the square.
Research conducted by
Glicksberg, Irving Leonard and Oliver Alfred Gross, Optimal Sets for Games Over the Square. Santa Monica, CA: RAND Corporation, 1952. https://www.rand.org/pubs/research_memoranda/RM889.html. Also available in print form.
Glicksberg, Irving Leonard and Oliver Alfred Gross, Optimal Sets for Games Over the Square, Santa Monica, Calif.: RAND Corporation, RM-889, 1952. As of June 16, 2021: https://www.rand.org/pubs/research_memoranda/RM889.html