Function space

Supremum metric

The supremum metric is the metric induced by the Uniform norm of a Function space of bound functions. It is the supremum of distances between corresponding values of the two functions. For bounded functions on the domain 𝐷

𝑑(𝑓,𝑔)=𝑓𝑔=sup{|𝑓(𝑥)𝑔(𝑥)|:𝑥𝐷}

This defines a Metric space for sets of real or complex valued continuous functions.

See also


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