Definition:Additive Function


 * Additive Function (Conventional Definition): $$f \left({x + y}\right) = f \left({x}\right) + f \left({y}\right)$$


 * Additive Function (Number Theory): If $$x \perp y$$ then $$f \left({x y}\right) = f \left({x}\right) + f \left({y}\right)$$
 * In this context, also see Completely Additive Function.

In measure theory, the concept has a completely different meaning:


 * Additive Function (Measure Theory): $$A \cap B = \varnothing \implies f \left({A \cup B}\right) = f \left({A}\right) + f \left({B}\right)$$
 * In this context, also see Sigma-Additive Function.