Jacob's ladders and properties of complete additivity and complete   multiplicativity in the set of reverse iterated integrals (energies)
  New class of integral identities concerning constraints on behavior of the Riemann's zeta function on the critical line is introduced in this paper. Namely, we have obtained new kind of $\sigma$-additivity and $\sigma$-multiplicativity in the class of reverse iterated integrals (energies). 
Jan Moser
math.CA