Function space

Uniform norm

Uniform norm¹ is a norm on a Function space defined as the supremum of a function on its domain. topology For the space 𝐶(𝐼), the uniform norm of a function 𝑓 :𝐼 →ℂ

‖𝑓‖∞=sup{|𝑓(𝑥)|:𝑥∈𝐼}

The metric induces is the Supremum metric, which is used to define Uniform convergence. As suggested by the notation, the uniform norm is a limit of the [[Lebesgue space|𝑝-norm]] as 𝑝 →∞.

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Footnotes

1. Also called sup norm, Chebyshev norm, or infinity norm ↩