Basic Analysis I — Real Analysis · Problem 5.2.17

The Riemann Integral — Jiri Lebl

Mathematics — Real Analysis · lipschitz-continuity

Problem

Suppose

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

is continuous and

g : \mathbb{R} \to \mathbb{R}

is Lipschitz continuous. Define

h(x) := \int_a^b g(t-x)f(t)\,dt.

Prove that

h

is Lipschitz continuous.