let X be set ; :: thesis: for S being SigmaField of X

for M being sigma_Measure of S holds {} is thin of M

let S be SigmaField of X; :: thesis: for M being sigma_Measure of S holds {} is thin of M

let M be sigma_Measure of S; :: thesis: {} is thin of M

set E0 = {} ;

A1: {} in S by MEASURE1:7;

M . {} = 0 by VALUED_0:def 19;

hence {} is thin of M by A1, MEASURE3:def 2; :: thesis: verum

for M being sigma_Measure of S holds {} is thin of M

let S be SigmaField of X; :: thesis: for M being sigma_Measure of S holds {} is thin of M

let M be sigma_Measure of S; :: thesis: {} is thin of M

set E0 = {} ;

A1: {} in S by MEASURE1:7;

M . {} = 0 by VALUED_0:def 19;

hence {} is thin of M by A1, MEASURE3:def 2; :: thesis: verum