1 2 1 1 convention F = F = F (which may or may not equal F = VF or F2 = VF2) t 1 2 We then set Ft = F F and verify that this family satisfies st s the usual conditions. 1 2 1) Each Fst contains the P-negligible sets, since Fs, F contain them for all s,t. 2) If (s,t) S (s',t'), then Ft C F t.. 1 1 2 2 In fact, F1 C F since sSs', F2 C F, since t5t', hence s s t t 1 2 1 F 2 Fst F (- F Fl C F OF Fs st s t S t st 3) We have F = ( F ,. (Note: In two parameters, st st (s,t)<(s',t') our usual definition of right limit is for (s,t) S (s',t'), (s,t) (s',t'), as we shall see later. The statement we shall prove is somewhat stronger.) Proof. One containment is evident: since FstC Fs t, for each (s',t') > (s,t) by (2), Fs C f Fst t (s,t)<(s',t') For the other containment, let A c n F = (F nFi). (s,t)<(s',t') s'>s t'>t Then A E F for all s'>s, hence A E Sn F = F SS '>s Similarly, A c F2 for all t'>t, hence A E } F2 = F2 t s t'>t Putting the two containments together gives the equality.