let X be non empty set ; :: thesis: for S being SigmaField of X
for E being Element of S
for f being PartFunc of X,REAL st E = {} holds
f is E -measurable
let S be SigmaField of X; :: thesis: for E being Element of S
for f being PartFunc of X,REAL st E = {} holds
f is E -measurable
let E be Element of S; :: thesis: for f being PartFunc of X,REAL st E = {} holds
f is E -measurable
let f be PartFunc of X,REAL; :: thesis: ( E = {} implies f is E -measurable )
assume E = {} ; :: thesis: f is E -measurable
then R_EAL f is E -measurable by Th29;
hence f is E -measurable by MESFUNC6:def 1; :: thesis: verum