I am stumped on trying to solve the following exercise:
Let f be a measurable function in E which can be expressed as $$ f = g +h$$ Where g is finite and integrable over E and h is nonnegative on E. Define $$ \int_{E}^{} f=\int_{E}^{} g+\int_{E}^{} h $$ Show that this is properly defined in the sense that it is independent of the particular choice of finite integrable function g and nonnegative function h whose sum is f.
Any thoughts would be greatly appreciated.