let X be non empty set ; :: thesis: for S being semialgebra_of_sets of X
for P being pre-Measure of S
for m being induced_Measure of S,P
for M being induced_sigma_Measure of S,m holds M is_extension_of m
let S be semialgebra_of_sets of X; :: thesis: for P being pre-Measure of S
for m being induced_Measure of S,P
for M being induced_sigma_Measure of S,m holds M is_extension_of m
let P be pre-Measure of S; :: thesis: for m being induced_Measure of S,P
for M being induced_sigma_Measure of S,m holds M is_extension_of m
let m be induced_Measure of S,P; :: thesis: for M being induced_sigma_Measure of S,m holds M is_extension_of m
let M be induced_sigma_Measure of S,m; :: thesis: M is_extension_of m
m is completely-additive by Th60;
then consider N being sigma_Measure of (sigma (Field_generated_by S)) such that
A2: ( N is_extension_of m & N = (sigma_Meas (C_Meas m)) | (sigma (Field_generated_by S)) ) by MEASURE8:33;
thus M is_extension_of m by A2, Def10; :: thesis: verum