Measure, Integration & Real Analysis · Problem 1A.13

Measures — Sheldon Axler

Mathematics — Measure Theory · riemann-integrable-increasing-function

Problem

Suppose

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

is an increasing function, meaning that

c, d \in [a, b]

with

c < d

implies

f(c) \leq f(d)

. Prove that

f

is Riemann integrable on

[a, b]