Inclusive scattering matrix closely related to inclusive cross-sections is defined in much more general situations than conventional scattering matrix. It contains the same information when the latter is well defined. It seems that the most natural description of scattering in quantum electrodynamics is based on inclusive scattering matrix. I'll discuss the general definition of inclusive scattering matrix in the framework of geometric approach to quantum theory and its expression in terms of generalized Green functions that appear in Keldysh formalism. I'll briefly explain the formalism of $L$-functionals and the definition of inclusive scattering matrix in terms of adiabatic $S$-matrix in this formalism.