let Omega be non empty set ; :: thesis: for Sigma being SigmaField of Omega
for f, g being Real-Valued-Random-Variable of Sigma holds f + g is Real-Valued-Random-Variable of Sigma
let Sigma be SigmaField of Omega; :: thesis: for f, g being Real-Valued-Random-Variable of Sigma holds f + g is Real-Valued-Random-Variable of Sigma
let f, g be Real-Valued-Random-Variable of Sigma; :: thesis: f + g is Real-Valued-Random-Variable of Sigma
( f is [#] Sigma -measurable & g is [#] Sigma -measurable ) by Def2;
then f + g is [#] Sigma -measurable by MESFUNC6:26;
hence f + g is Real-Valued-Random-Variable of Sigma by Def2; :: thesis: verum