Universal Alignment Probability Revisited

We found a minor error in the proof of paper “Universal Alignment Probability Revisited” by S.Y. Lin and Y.C. Ho (J. Optim. Theory Appl. 113(2):399–407, 2002). In this note, we give a counterexample and explain the reason. We also show that the conclusion of that paper is still correct despite this minor error. A new proof of the conclusion is given. This work was supported by NSFC Grants 60574067, 60704008, 60721003 and 60736027, NCET Program NCET-04-0094 of China, National New Faculty Funding for Universities with Doctoral Program 20070003110, Program of Introducing Talents of Discipline to Universities (National 111 International Collaboration Project) B06002, and High-Level Graduate Student Scholarship 2007 of China Scholarship Council.