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,ExtREAL 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,ExtREAL 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,ExtREAL st f is_integrable_on M & g is_integrable_on M holds
dom (f + g) in S
let f, g be PartFunc of X,ExtREAL ; :: 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 ( f " {+infty } in S & f " {-infty } in S & g " {+infty } in S & g " {-infty } in S & ex E1 being Element of S st
( E1 = dom f & f is_measurable_on E1 ) & ex E2 being Element of S st
( E2 = dom g & g is_measurable_on E2 ) ) by Def17, Th111;
hence dom (f + g) in S by Th52; :: thesis: verum