let X be set ; :: thesis: for S being SigmaField of X
for M being sigma_Measure of S
for A, B being Element of S st A c= B & M . A < +infty holds
M . (B \ A) = (M . B) - (M . A)
let S be SigmaField of X; :: thesis: for M being sigma_Measure of S
for A, B being Element of S st A c= B & M . A < +infty holds
M . (B \ A) = (M . B) - (M . A)
let M be sigma_Measure of S; :: thesis: for A, B being Element of S st A c= B & M . A < +infty holds
M . (B \ A) = (M . B) - (M . A)
let A, B be Element of S; :: thesis: ( A c= B & M . A < +infty implies M . (B \ A) = (M . B) - (M . A) )
assume A1: ( A c= B & M . A < +infty ) ; :: thesis: M . (B \ A) = (M . B) - (M . A)
M is Measure of S by Th60;
hence M . (B \ A) = (M . B) - (M . A) by A1, Th26; :: thesis: verum