let Omega be non empty set ; :: thesis: for Sigma being SigmaField of Omega
for f being Real-Valued-Random-Variable of Sigma holds abs f is Real-Valued-Random-Variable of Sigma
let Sigma be SigmaField of Omega; :: thesis: for f being Real-Valued-Random-Variable of Sigma holds abs f is Real-Valued-Random-Variable of Sigma
let f be Real-Valued-Random-Variable of Sigma; :: thesis: abs f is Real-Valued-Random-Variable of Sigma
consider X being Element of Sigma such that
P1: ( X = Omega & f is_measurable_on X ) by def1;
P3: dom f = X by FUNCT_2:def 1, P1;
R_EAL f is_measurable_on X by P1, MESFUNC6:def 6;
then |.(R_EAL f).| is_measurable_on X by P3, MESFUNC2:29;
then R_EAL (abs f) is_measurable_on X by MESFUNC6:1;
then abs f is_measurable_on X by MESFUNC6:def 6;
hence abs f is Real-Valued-Random-Variable of Sigma by def1, P1; :: thesis: verum