let X be non empty set ; :: thesis: for S being SigmaField of X
for M being sigma_Measure of S
for f being PartFunc of X,REAL st dom f = {} holds
Integral (M,f) = 0
let S be SigmaField of X; :: thesis: for M being sigma_Measure of S
for f being PartFunc of X,REAL st dom f = {} holds
Integral (M,f) = 0
let M be sigma_Measure of S; :: thesis: for f being PartFunc of X,REAL st dom f = {} holds
Integral (M,f) = 0
let f be PartFunc of X,REAL; :: thesis: ( dom f = {} implies Integral (M,f) = 0 )
assume dom f = {} ; :: thesis: Integral (M,f) = 0
then dom (R_EAL f) = {} by MESFUNC5:def 7;
hence Integral (M,f) = 0 by Th1; :: thesis: verum