Measure, Integration & Real Analysis · Problem 1B.2

Measures — Sheldon Axler

Mathematics — Measure Theory · riemann-integrable-lower-upper-criterion

Problem

Suppose

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

is a bounded function. Prove that

f

is Riemann integrable if and only if

L(-f, [a, b]) = -L(f, [a, b]).