
theorem Th27:
for X be set, S be SigmaField of X, M be sigma_Measure of S,
 E be Element of S holds E is Element of COM(S,M)
proof
    let X be set, S be SigmaField of X, M be sigma_Measure of S,
    E be Element of S;

    reconsider E0 = {} as Element of S by MEASURE1:7;
    M.E0 = 0 by VALUED_0:def 19; then
A1: E0 is thin of M by MEASURE3:def 2;

    E = E \/ E0;
    hence E is Element of COM(S,M) by A1,MEASURE3:def 3;
end;
