Basic Analysis I — Real Analysis · Problem 3.2.15

Continuous Functions — Jiri Lebl

Mathematics — Real Analysis · continuous-functions

Problem

Suppose

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

is a continuous function such that

g(0) = 0

, and suppose

f : \mathbb{R} \to \mathbb{R}

is such that

\bigl|f(x) - f(y)\bigr| \leq g(x - y)

for all

x

and

y

. Show that

f

is continuous.