Measure, Integration & Real Analysis · Problem 1A.4

Measures — Sheldon Axler

Mathematics — Measure Theory · riemann-integral-sum-of-functions

Problem

Suppose

f, g : [a, b] \to \mathbf{R}

are Riemann integrable. Prove that

f + g

is Riemann integrable on

[a, b]

and

\int_a^b (f + g) = \int_a^b f + \int_a^b g.