Measure, Integration & Real Analysis · Problem 1A.9

Measures — Sheldon Axler

Mathematics — Measure Theory · riemann-integrable-subinterval

Problem

Suppose

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

is Riemann integrable. Prove that if

c, d \in \mathbf{R}

and

a \leq c < d \leq b

, then

f

is Riemann integrable on

[c, d]

. [To say that

f

is Riemann integrable on

[c, d]

means that

f

with its domain restricted to

[c, d]

is Riemann integrable.]