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Extreme value theorem
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Supremum norm
Created
2026-09-24
Updated
2026-10-03
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The
supremum norm
of
a
bounded real- or complex-valued
function
on
a
set
X
is
∥
f
∥
∞
=
sup
x
∈
X
∣
f
(
x
)
∣.
(1)
For
a
continuous function
on
a
compact space
, the
extreme value theorem
makes this
supremum
a
maximum.
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