reserve X for non empty set,
        x for Element of X,
        S for SigmaField of X,
        M for sigma_Measure of S,
        f,g,f1,g1 for PartFunc of X,REAL,
        l,m,n,n1,n2 for Nat,
        a,b,c for Real;
reserve k for positive Real;
reserve v,u for VECTOR of RLSp_LpFunct(M,k);

theorem
0.(RLSp_LpFunct(M,k)) = X-->0 &
0.(RLSp_LpFunct(M,k)) in AlmostZeroLpFunctions(M,k)
proof
   thus 0.(RLSp_LpFunct(M,k)) = X --> 0 by Th23,SUBSET_1:def 8;
A1:X-->0 a.e.= X-->0,M & X --> 0 in Lp_Functions(M,k) by Th23,LPSPACE1:28;
   0.(RLSp_LpFunct(M,k)) = 0.(RLSp_PFunctX) by Th23,SUBSET_1:def 8;
   hence 0.(RLSp_LpFunct(M,k)) in AlmostZeroLpFunctions(M,k) by A1;
end;
