Basic Analysis I — Real Analysis · Problem 6.1.1

Sequences of Functions — Jiri Lebl

Mathematics — Real Analysis · uniform-norm-triangle-inequality

Problem

Let

f

and

g

be bounded functions on

[a, b]

. Prove

\|f + g\|_{[a,b]} \leq \|f\|_{[a,b]} + \|g\|_{[a,b]}.