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);
reserve v,u for VECTOR of RLSp_AlmostZeroLpFunct(M,k);

theorem Th35:
f in Lp_Functions(M,k) implies
 ex E be Element of S st M.(E`) = 0 & dom f = E & f is E-measurable
proof
   assume f in Lp_Functions(M,k); then
   ex f1 be PartFunc of X,REAL st f = f1 &
    (ex E be Element of S st M.(E`) = 0 & dom f1 = E &
     f1 is E-measurable & (abs f1) to_power k is_integrable_on M);
   hence thesis;
end;
