let X be non empty set ; :: thesis: for S being SigmaField of X
for M being sigma_Measure of S
for f, g being PartFunc of X,REAL st f is_integrable_on M & g is_integrable_on M holds
dom (f + g) in S
let S be SigmaField of X; :: thesis: for M being sigma_Measure of S
for f, g being PartFunc of X,REAL st f is_integrable_on M & g is_integrable_on M holds
dom (f + g) in S
let M be sigma_Measure of S; :: thesis: for f, g being PartFunc of X,REAL st f is_integrable_on M & g is_integrable_on M holds
dom (f + g) in S
let f, g be PartFunc of X,REAL; :: thesis: ( f is_integrable_on M & g is_integrable_on M implies dom (f + g) in S )
assume ( f is_integrable_on M & g is_integrable_on M ) ; :: thesis: dom (f + g) in S
then ( R_EAL f is_integrable_on M & R_EAL g is_integrable_on M ) ;
then dom ((R_EAL f) + (R_EAL g)) in S by MESFUNC5:107;
then dom (R_EAL (f + g)) in S by Th23;
hence dom (f + g) in S ; :: thesis: verum