let X be non empty set ; :: thesis: for S being SigmaField of X
for f, g being PartFunc of X,REAL
for A being Element of S st A c= dom f & f is A -measurable & g is A -measurable holds
(max+ (f + g)) + (max- f) is A -measurable
let S be SigmaField of X; :: thesis: for f, g being PartFunc of X,REAL
for A being Element of S st A c= dom f & f is A -measurable & g is A -measurable holds
(max+ (f + g)) + (max- f) is A -measurable
let f, g be PartFunc of X,REAL; :: thesis: for A being Element of S st A c= dom f & f is A -measurable & g is A -measurable holds
(max+ (f + g)) + (max- f) is A -measurable
let A be Element of S; :: thesis: ( A c= dom f & f is A -measurable & g is A -measurable implies (max+ (f + g)) + (max- f) is A -measurable )
assume that
A1: A c= dom f and
A2: f is A -measurable and
A3: g is A -measurable ; :: thesis: (max+ (f + g)) + (max- f) is A -measurable
f + g is A -measurable by A2, A3, Th26;
then A4: max+ (f + g) is A -measurable by Th46;
max- f is A -measurable by A1, A2, Th47;
hence (max+ (f + g)) + (max- f) is A -measurable by A4, Th26; :: thesis: verum