A real-valued function f : X → ℝ on X can be expressed as f = f+ − f−, where the nonnegative functions f+: X → ℝ and f−: X → ℝ are the positive and negative parts of f. If f is measurable, then so are f+ and f− (Proposition 1.6). Integration of measurable real-valued functions, leading to real-valued integrals, is considered by using the above decomposition.