(参考) https://mathoverflow.net/questions/151286/probabilities-in-a-riddle-involving-axiom-of-choice Probabilities in a riddle involving axiom of choice Denis氏 Dec 9 '13 DR Pruss氏
By a conglomerability assumption, we could then conclude that P(X<=Y)=0, which would be absurd as the same reasoning would also show that P(Y<=X)=0.
http://www.mdpi.com/2073-8994/3/3/636 Symmetry and the Brown-Freiling Refutation of the Continuum Hypothesis by Paul Bartha Symmetry 2011, 3(3), 636-652; []