Measure, Integration & Real Analysis · Problem 1A.12

Measures — Sheldon Axler

Mathematics — Measure Theory · riemann-integral-absolute-value

Problem

Suppose f:[a,b]→Rf : [a, b] \to \mathbf{R} is Riemann integrable. Prove that ∣f∣|f| is Riemann integrable and that ∣∫abf∣≤∫ab∣f∣.\left|\int_a^b f\right| \leq \int_a^b |f|.

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