It is well known that many processes in Mechanic, Physics, Economy, Biology and other sciences can be represented by operators. It is also known that many classical problems for differential equations usually involve local operators which some of them can be represented as nonlinear Nemytskii operator. This is an example of local operator which we concentrated the majority attention on this module. The Theory of Functional Differential Equations also involves inner superposition and integral operators, which are examples of disjointness-preserving and addictive orthogonally operators. These two operators was considered on this work. We also introduced the notion of partially disjointness-preserving operator. We analyzed general properties and the representation of all these operators on the space of measurable functions. Furthermore, we related one to another.