let Omega1, Omega2 be non empty set ; :: thesis: for S1 being SigmaField of Omega1
for S2 being SigmaField of Omega2
for P being Probability of S1
for F being random_variable of S1,S2 holds (image_measure (F,(P2M P))) . Omega2 = 1
let S1 be SigmaField of Omega1; :: thesis: for S2 being SigmaField of Omega2
for P being Probability of S1
for F being random_variable of S1,S2 holds (image_measure (F,(P2M P))) . Omega2 = 1
let S2 be SigmaField of Omega2; :: thesis: for P being Probability of S1
for F being random_variable of S1,S2 holds (image_measure (F,(P2M P))) . Omega2 = 1
let P be Probability of S1; :: thesis: for F being random_variable of S1,S2 holds (image_measure (F,(P2M P))) . Omega2 = 1
let F be random_variable of S1,S2; :: thesis: (image_measure (F,(P2M P))) . Omega2 = 1
A1: for y being set st y in S2 holds
(image_measure (F,(P2M P))) . y = (P2M P) . (F " y) by Def6;
thus (image_measure (F,(P2M P))) . Omega2 = (P2M P) . (F " Omega2) by PROB_1:5, A1
.= (P2M P) . Omega1 by FUNCT_2:40
.= 1 by PROB_1:def 8 ; :: thesis: verum