Function space

Uniform norm

Uniform norm1 is a norm on a Function space defined as the supremum of a function on its domain. #m/def/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 𝑝-norm as 𝑝 →∞.

#state/tidy | #lang/en | #SemBr

Footnotes

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