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Lebl-Basic-Analysis-I
· Problem 6.1.5
Sequences of Functions
Mathematics · uniform-convergence-sums
Problem
Suppose
{
f
n
}
n
=
1
∞
\{f_n\}_{n=1}^\infty
{
f
n
}
n
=
1
∞
and
{
g
n
}
n
=
1
∞
\{g_n\}_{n=1}^\infty
{
g
n
}
n
=
1
∞
defined on some set
A
A
A
converge to
f
f
f
and
g
g
g
respectively uniformly on
A
A
A
. Show that
{
f
n
+
g
n
}
n
=
1
∞
\{f_n + g_n\}_{n=1}^\infty
{
f
n
+
g
n
}
n
=
1
∞
converges uniformly to
f
+
g
f+g
f
+
g
on
A
A
A
.
Related theory
Series Convergence Tests And Absolute Convergence
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