Dynkin games in a general framework

and j and z are left limited along stopping times at T with fjðT 2Þ 1⁄4 zðT 2Þ} 1⁄4 Y a.s. (and the same remark holds in the case of processes, that is Theorem B.4). Similarly, in Lemma 4.6, the first equality holds a.s. on ft , T} and the second equality on fu , T}. Also, at the end of the proof of Theorem 4.3, the two inequalities concerning E1⁄2Jðu2Þ1C and E1⁄2J0ðu2Þ1C are precised as follows: E1⁄2Jðu2Þ1C # 1⁄2E1⁄2J0ðu2Þ1C þ E1⁄2jðuÞ1C>fu,T} þ E1⁄2jðT Þ1C>fu1⁄4T} ; E1⁄2J 0ðu2Þ1C # 1⁄2E1⁄2Jðu2Þ1C 2 E1⁄2zðuÞ1C>fu,T} 2 E1⁄2zðT Þ1C>fu1⁄4T} ;