The review of results on the theory of the linear order continuous operators in semi-ordered spaces of measurable functions

The review of researches on the theory of the linear order continuous operators in vector lattices and spaces of measurable functions is this. Explicitly are considered: theorem of pseudo-integral repre-sentation, types of operators: integral, diffusion, singular and atomic. Also questions of applications are considered: spectra, Fredholm operators, algebraic properties "the continuous on a measure" op-erators, a condition of integral of the operator Green of the general boundary value problem.