Basic Analysis I — Real Analysis · Problem 5.1.15

The Riemann Integral — Jiri Lebl

Mathematics — Real Analysis · darboux-sums

Problem

Suppose that

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

is a bounded function, and

P

is a partition of

[a,b]

such that

L(P,f) = U(P,f)

. Prove that

f

is a constant function.