reserve a,b,r for Real;
reserve A,B for non empty set;
reserve f,g,h for Element of PFuncs(A,REAL);
reserve u,v,w for VECTOR of RLSp_PFunctA;
reserve X for non empty set,
  x for Element of X,
  S for SigmaField of X,
  M for sigma_Measure of S,
  E,E1,E2 for Element of S,
  f,g,h,f1,g1 for PartFunc of X ,REAL;
reserve v,u for VECTOR of RLSp_L1Funct M;

theorem
  0.(RLSp_L1Funct M) = X-->0 & 0.(RLSp_L1Funct M) in AlmostZeroFunctions M
proof
  thus 0.(RLSp_L1Funct M) = X --> 0 by Lm3,SUBSET_1:def 8;
  X-->0 a.e.= X-->0,M & 0.(RLSp_L1Funct M) = 0.(RLSp_PFunctX) by Lm3,Th28,
SUBSET_1:def 8;
  hence thesis;
end;
