theorem Th73:
for X be non empty set, S be SigmaField of X,
 M be sigma_Measure of S holds zeroCoset M = zeroCoset(M,1)
proof
   let X be non empty set;
   let S be SigmaField of X;
   let M be sigma_Measure of S;
   reconsider z = zeroCoset(M,1) as Element of CosetSet M by Th71;
   X-->0 in Lp_Functions(M,1) by Th23; then
   ex E be Element of S st
    M.E`=0 & dom (X-->0) = E & (X-->0) is E-measurable by Th35; then
A1:z = a.e-eq-class(X-->0,M) by Lm12;
   X-->0 in L1_Functions M by Th56;
   hence thesis by A1,LPSPACE1:def 16;
end;
