Sup norms

In mathematical analysis, the uniform norm (or sup norm) assigns to real- or complex-valued bounded functions f defined on a set S the non-negative number

This norm is also called the supremum norm, the Chebyshev norm, or the infinity norm. The name "uniform norm" derives from the fact that a sequence of functions ${\displaystyle \{f_{n}\}}$ converges to f under the metric derived from the uniform norm if and only if ${\displaystyle f_{n}}$ converges to ${\displaystyle f}$ uniformly.

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