Basic Analysis I — Real Analysis · Problem 5.2.14

The Riemann Integral — Jiri Lebl

Mathematics — Real Analysis · monotone-functions-integrability

Problem

Let

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

be a function. a) Show that if

f

is increasing, then it is Riemann integrable. Hint: Use a uniform partition; each subinterval of same length. b) Use part a) to show that if

f

is decreasing, then it is Riemann integrable. c) Suppose

h = f - g

where

f

and

g

are increasing functions on

[a,b]

. Show that

h

is Riemann integrable.