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Lebl-Basic-Analysis-I
· Problem 6.1.3
Sequences of Functions
Mathematics · uniform-convergence-restriction
Problem
Suppose
f
n
:
S
→
R
f_n : S \to \mathbb{R}
f
n
:
S
→
R
are functions that converge uniformly to
f
:
S
→
R
f : S \to \mathbb{R}
f
:
S
→
R
. Suppose
A
⊂
S
A \subset S
A
⊂
S
. Show that the sequence of restrictions
{
f
n
∣
A
}
n
=
1
∞
\{f_n|_A\}_{n=1}^\infty
{
f
n
∣
A
}
n
=
1
∞
converges uniformly to
f
∣
A
f|_A
f
∣
A
.
Related theory
Series Convergence Tests And Absolute Convergence
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