Basic Analysis I — Real Analysis · Problem 6.1.4

Sequences of Functions — Jiri Lebl

Mathematics — Real Analysis · pointwise-convergence-sums

Problem

Suppose

\{f_n\}_{n=1}^\infty

and

\{g_n\}_{n=1}^\infty

defined on some set

A

converge to

f

and

g

respectively pointwise. Show that

\{f_n + g_n\}_{n=1}^\infty

converges pointwise to

f + g