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Lebl-Basic-Analysis-I
· Problem 6.1.1
Sequences of Functions
Mathematics · uniform-norm-triangle-inequality
Problem
Let
f
f
f
and
g
g
g
be bounded functions on
[
a
,
b
]
[a,b]
[
a
,
b
]
. Prove
∥
f
+
g
∥
[
a
,
b
]
≤
∥
f
∥
[
a
,
b
]
+
∥
g
∥
[
a
,
b
]
\|f+g\|_{[a,b]} \leq \|f\|_{[a,b]} + \|g\|_{[a,b]}
∥
f
+
g
∥
[
a
,
b
]
≤
∥
f
∥
[
a
,
b
]
+
∥
g
∥
[
a
,
b
]
.
Related theory
The Triangle Inequality And Norm Properties
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