Let (X,m,mu),(Y,N,v) be measure spaces, suppose that M contains a
non-empty mu null set and that N notequal to P(Y). Then
(XxY,MxN,muxv)is not complete . conclude that
(R2,L1xL1,lambda1xlambda1) is not complete.

  here L1 denotes the lebesgue sigma algbera in R1 , lambda1 the
lebesgue measure on L1.