Basic Analysis I — Real Analysis · Problem 5.1.14

The Riemann Integral — Jiri Lebl

Mathematics — Real Analysis · riemann-integrability

Problem

(Challenging) Construct functions

f

and

g

, where

f : [0,1] \to \mathbb{R}

is Riemann integrable,

g : [0,1] \to [0,1]

is one-to-one and onto, and such that the composition

f \circ g

is not Riemann integrable.