let X be non empty set ; :: thesis: for S being SigmaField of X
for M being sigma_Measure of S
for F being SetSequence of S st F is convergent holds
ex G being Function of NAT,S st
( G = inferior_setsequence F & M . (lim F) = sup (rng (M * G)) )
let S be SigmaField of X; :: thesis: for M being sigma_Measure of S
for F being SetSequence of S st F is convergent holds
ex G being Function of NAT,S st
( G = inferior_setsequence F & M . (lim F) = sup (rng (M * G)) )
let M be sigma_Measure of S; :: thesis: for F being SetSequence of S st F is convergent holds
ex G being Function of NAT,S st
( G = inferior_setsequence F & M . (lim F) = sup (rng (M * G)) )
let F be SetSequence of S; :: thesis: ( F is convergent implies ex G being Function of NAT,S st
( G = inferior_setsequence F & M . (lim F) = sup (rng (M * G)) ) )
assume F is convergent ; :: thesis: ex G being Function of NAT,S st
( G = inferior_setsequence F & M . (lim F) = sup (rng (M * G)) )
then lim_inf F = lim F by KURATO_0:def 5;
hence ex G being Function of NAT,S st
( G = inferior_setsequence F & M . (lim F) = sup (rng (M * G)) ) by Th3; :: thesis: verum