Basic Analysis I — Real Analysis · Problem 6.1.5

Sequences of Functions — Jiri Lebl

Mathematics — Real Analysis · uniform-convergence-sums

Problem

Suppose {fn}n=1∞\{f_n\}_{n=1}^\infty and {gn}n=1∞\{g_n\}_{n=1}^\infty defined on some set AA converge to ff and gg respectively uniformly on AA. Show that {fn+gn}n=1∞\{f_n + g_n\}_{n=1}^\infty converges uniformly to f+gf + g on AA.

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