
theorem Th31:
for r be Real, E be Element of L-Field, f be PartFunc of REAL,ExtREAL
 st E = {r} holds f is E-measurable
proof
    let r be Real, E be Element of L-Field, f be PartFunc of REAL,ExtREAL;
    assume A1: E = {r};
    for a be Real holds E /\ less_dom(f,a) in L-Field
    proof
     let a be Real;
     E /\ less_dom(f,a) = {} or E /\ less_dom(f,a) = {r}
       by A1,XBOOLE_1:17,ZFMISC_1:33;
     hence thesis by A1,MEASURE1:7;
    end;
    hence f is E-measurable by MESFUNC1:def 16;
end;
